If $x=a,\ y=b$ is the solution of the pair of equations $x-y=2$ and $x+y=4$, find the value of $a$ and $b$.

Given: $x=a,\ y=b$ is the solution of the pair of equations $x-y=2$ and $x+y=4$.

To do: To find the value of $a$ and $b$.

Solution: 
 Given pair of linear equations-


$x−y=2.....(1)$

$x+y=4.....(2)$

Adding equation $( 1)$ and $( 2)$, we have

$(x−y)+(x+y)=2+4$

$x−y+x+y=6$

$2x=6$

$\Rightarrow x=\frac{6}{2}$ 

​$\Rightarrow x=3$

Substituting the value of $x$ in equation $( 1)$, we have

$3−y=2$

$\Rightarrow y=3−2=1$

Hence the values of $a$ and $b$ are $1$ and $2$ respectively.

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Updated on: 10-Oct-2022

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