Question

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

Answer 1

Given pair of linear equations-

$x-y=2.....\left(1\right)$

$x+y=4.....\left(2\right)$

Adding equation $\left(1\right)$ and $\left(2\right)$, we have

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

$x-y+x+y=6$

$2x=6$

$\Rightarrow x=\frac{6}{2}=3$

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

$3-y=2$

$\Rightarrow y=3-2=1$

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