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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