Answer
The solution is $(19,16)$.
Work Step by Step
The given system of equations is
$10x-9y=46$ ...... (1)
$-2x+3y=10$ ...... (2)
Multiply each side of equation (2) by $3$.
$3(-2x+3y)=3(10)$
Simplify.
$-6x+9y=30$ ...... (3)
Add equation (1) and (3).
$\Rightarrow 10x-9y-6x+9y=46+30$
Add like terms.
$\Rightarrow 4x=76$
Divide each side by $4$.
$\Rightarrow \frac{4x}{4}=\frac{76}{4}$
Simplify.
$\Rightarrow x=19$
Substitute $19$ for $x$ in equation (2).
$\Rightarrow -2(19)+3y=10$
Simplify.
$\Rightarrow -38+3y=10$
Add $38$ to each side.
$\Rightarrow -38+3y+38=10+38$
Simplify.
$\Rightarrow 3y=48$
Divide each side by $3$.
$\Rightarrow \frac{3y}{3}=\frac{48}{3}$
Simplify.
$\Rightarrow y=16$
Check $(x,y)=(19,16)$
Equation (1):
$\Rightarrow 10x-9y=46$
$\Rightarrow 10(19)-9(16)=46$
$\Rightarrow 190-144=46$
$\Rightarrow 46=46$
True.
Equation (2):
$\Rightarrow -2x+3y=10$
$\Rightarrow -2(19)+3(16)=10$
$\Rightarrow -38+48=10$
$\Rightarrow 10=10$
True.
Hence, the solution is $(19,16)$.
