Answer
The solution is $(1,2)$.
Work Step by Step
The given system of equations is
$3x+2y=7$ ...... (1)
$-3x+4y=5$ ...... (2)
Add equation (1) and (2).
$\Rightarrow 3x+2y-3x+4y=7+5$
Add like terms.
$\Rightarrow 6y=12$
Divide each side by $6$.
$\Rightarrow \frac{6y}{6}=\frac{12}{6}$
Simplify.
$\Rightarrow y=2$
Substitute $2$ for $y$ equation (1).
$\Rightarrow 3x+2(2)=7$
Simplify.
$\Rightarrow 3x+4=7$
Subtract $4$ from each side.
$\Rightarrow 3x+4-4=7-4$
Simplify.
$\Rightarrow 3x=3$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{3}{3}$
Simplify.
$\Rightarrow x=1$.
Check (x,y)=(1,2)
Equation (1):
$\Rightarrow 3x+2y=7$
$\Rightarrow 3(1)+2(2)=7$
$\Rightarrow 3+4=7$
$\Rightarrow 7=7$
True.
Equation (2):
$\Rightarrow -3x+4y=5$
$\Rightarrow -3(1)+4(2)=5$
$\Rightarrow -3+8=5$
$\Rightarrow 5=5$
True.
Hence, the solution is $(1,2)$.
