Answer
The solution is $(1,1)$.
Work Step by Step
The given system of equations is
$x+y=2$ ...... (1)
$2x+7y=9$ ...... (2)
Multiply each side of equation (1) by $-2$.
$-2(x+y)=-2(2)$
Simplify.
$-2x-2y=-4$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 2x+7y-2x-2y=9-4$
Add like terms.
$\Rightarrow 5y=5$
Divide each side by $5$.
$\Rightarrow \frac{5y}{5}=\frac{5}{5}$
Simplify.
$\Rightarrow y=1$
Substitute $1$ for $y$ in equation (1).
$\Rightarrow x+1=2$
Subtract $1$ from each side.
$\Rightarrow x+1-1=2-1$
Simplify.
$\Rightarrow x=1$
Check $(x,y)=(1,1)$
Equation (1):
$\Rightarrow x+y=2$
$\Rightarrow 1+1=2$
$\Rightarrow 2=2$
True.
Equation (2):
$\Rightarrow 2x+7y=9$
$\Rightarrow 2(1)+7(1)=9$
$\Rightarrow 2+7=9$
$\Rightarrow 9=9$
True.
Hence, the solution is $(1,1)$.
