Answer
$(1, 3)$
Work Step by Step
Given system is-
$x +2y$ = $7$ __ eq.1
$5x -y$ = $2$ __ eq.2
Multiplying eq.2 by '2'-
$10x -2y$ = $4$ __ eq.3
Adding eq.1 and eq.3 -
$x +2y+10x -2y$ = $7+4$
i.e. $11x$ = $11$
i.e. $x$ = $\frac{11}{11}$
i.e. $x$ = $1$
Substituting for $x$ in eq.1
$1 +2y$ = $7$
i.e. $2y$ = $7-1$ =$6$
i.e. $y$ = $\frac{6}{2}$
i.e. $y$ = $3$
Thus $(1, 3)$ is the solution of given system.