Answer
$(x,y)=(-2,-5)$.
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
4&-3 &7 \\
0 & -1 & 5
\end{bmatrix}$.
For the linear equation.
First column $=$ coefficients of $x$.
Second column $=$ coefficients of $y$
and third column $=$ the right-hand side.
The given matrix is a upper triangular form.
Rewrite the second row as a linear equation.
$\Rightarrow 0x-1y=5$
$\Rightarrow -y=5$
Multiply the equation by $-1$.
$\Rightarrow -1(-y)=-1(5)$
Simplify.
$\Rightarrow y=-5$
Rewrite the first row as a linear equation.
$\Rightarrow 4x-3y=7$
Substitute $y=-5$.
$\Rightarrow 4x-3(-5)=7$
Clear the parentheses.
$\Rightarrow 4x+15=7$
Subtract $15$ from both sides.
$\Rightarrow 4x+15-15=7-15$
Simplify.
$\Rightarrow 4x=-8$
Divide both sides by $4$.
$\Rightarrow \frac{4x}{4}=\frac{-8}{4}$
Simplify.
$\Rightarrow x=-2$
The solution set is $(x,y)=(-2,-5)$.
