Answer
The system of linear equations has infinitely many solutions.
Work Step by Step
The given system of equations is
$-4x+4y=32$ ...... (1)
$3x+24=3y$ ...... (2)
Divide equation (1) by $4$.
$\Rightarrow \frac{-4x+4y}{4}=\frac{32}{4}$
Simplify.
$\Rightarrow -x+y=8$ ...... (3)
Divide equation (2) by $3$.
$\Rightarrow \frac{3x+24}{3}=\frac{3y}{3}$
Simplify.
$\Rightarrow x+8=y$ ...... (4)
Add equation (3) and (4).
$\Rightarrow -x+y+x+8=8+y$
Add like terms.
$\Rightarrow y+8=8+y$
The equation $ y+8=8+y$ is always true.
Hence, the system of linear equations has infinitely many solutions.
