Answer
The solution is $(2,1)$.
Work Step by Step
The given system of equations is
$8x-5y=11$ ...... (1)
$4x-3y=5$ ...... (2)
Multiply each side of equation (2) by $-2$.
$-2(4x-3y)=-2(5)$
Simplify.
$-8x+6y=-10$ ...... (3)
Add equation (1) and (3).
$\Rightarrow 8x-5y-8x+6y=11-10$
Add like terms.
$\Rightarrow y=1$
Substitute $1$ for $y$ in equation (1).
$\Rightarrow 8x-5(1)=11$
Simplify.
$\Rightarrow 8x-5=11$
Add $5$ to each side.
$\Rightarrow 8x-5+5=11+5$
Simplify.
$\Rightarrow 8x=16$
Divide each side by $8$.
$\Rightarrow \frac{8x}{8}=\frac{16}{8}$
Simplify.
$\Rightarrow x=2$
Check $(x,y)=(2,1)$
Equation (1):
$\Rightarrow 8x-5y=11$
$\Rightarrow 8(2)-5(1)=11$
$\Rightarrow 16-5=11$
$\Rightarrow 11=11$
True.
Equation (2):
$\Rightarrow 4x-3y=5$
$\Rightarrow 4(2)-3(1)=5$
$\Rightarrow 8-3=5$
$\Rightarrow 5=5$
True.
Hence, the solution is $(2,1)$.
