Linear Equations in One Variable - Solutions 3
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 2
Linear Equations in One Variable (Ex. 2.3)
NCERT Solutions
CHAPTER - 2
Linear Equations in One Variable (Ex. 2.3)
Solve the following equations and check your results.
1. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image001.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image001.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image001.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image001.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image003.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image004.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image006.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image007.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
2. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image008.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image008.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image008.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image008.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image009.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image010.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image011.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image012.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image013.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image014.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image015.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
3. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image016.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image016.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image016.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image016.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image017.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image019.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image020.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image021.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image022.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image023.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
4. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image024.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image024.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image024.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image024.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image025.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image026.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image027.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image028.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image029.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image030.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image031.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image032.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
5. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image033.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image033.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image033.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image033.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image034.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image035.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image036.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image037.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image038.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
6. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image039.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image039.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image040.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image040.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image041.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image042.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image043.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image044.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image045.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image046.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image047.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image048.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image049.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
7. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image050.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image050.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image051.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image051.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image052.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image053.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image054.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image055.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image056.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image057.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image058.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image059.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
8. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image060.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image060.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image060.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image060.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image061.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image062.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image063.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image064.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image065.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image066.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image067.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image068.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image069.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
9. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image070.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image070.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image070.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image070.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image071.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image072.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image073.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image074.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image075.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image076.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image077.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image078.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image079.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.
10. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image080.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image080.png)
Ans. ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image080.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image080.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image081.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image082.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image083.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image084.png)
To check:
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image085.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image086.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image087.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image088.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image089.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/2_3/image002.png)
Hence, it is correct.