Answer
$(x,y)=(\frac{7}{3},-2)$.
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
3&1 &5 \\
0 & 2 & -4
\end{bmatrix}$.
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.
$\Rightarrow 0x+2y=-4$
$\Rightarrow 2y=-4$
Divide the equation by $2$.
$\Rightarrow \frac{2y}{2}=\frac{-4}{2}$
Simplify.
$\Rightarrow y=-2$
Rewrite the first row as a linear equation.
$\Rightarrow 3x+1y=5$
$\Rightarrow 3x+y=5$
Substitute $y=-2$.
$\Rightarrow 3x+(-2)=5$
Clear the parentheses.
$\Rightarrow 3x-2=5$
Add $2$ to both sides.
$\Rightarrow 3x-2+2=5+2$
Simplify.
$\Rightarrow 3x=7$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}=\frac{7}{3}$
Simplify.
$\Rightarrow x=\frac{7}{3}$
The solution set is $(x,y)=(\frac{7}{3},-2)$.
