Answer
$\{(3,2)\}$.
Work Step by Step
The system contains two linear equations. We will graph each of them. The solution of the system is the point(s) of intersection between the two graphs.
Step 1:- Graph the first equation.
$\Rightarrow 2x-y=4$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow 2x-0=4$
Divide both sides by $2$.
$\Rightarrow x=2$
The $x−$intercept is $2$, so the line passes through $A=(2,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow 2(0)-y=4$
Simplify.
$\Rightarrow -y=4$
Multiply both sides by $-1$.
$\Rightarrow y=-4$
The $y−$intercept is $-4$, so the line passes through $B=(0,-4)$.
Draw a straight line through the points $A$ and $B$.
Step 2:- Graph the second equation.
$\Rightarrow x+y=5$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow x+0=5$
Simplify.
$\Rightarrow x=5$
The $x−$intercept is $5$, so the line passes through $C=(5,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow (0)+y=5$
Simplify.
$\Rightarrow y=5$
The $y−$intercept is $5$, so the line passes through $D=(0,5)$.
Draw a straight line through the points $C$ and $D$.
Step 3:- The intersection point.
Draw both lines on the same graph. The intersection point is the solution of the system.
The intersection point is $E=\{(3,2)\}$.
We check if $(3,2)$ checks the system of equations.
$$\begin{align*}
2x-y&=4\\
2(3)-2&\stackrel{?}{=}4\\
6-2&\stackrel{?}{=}4\\
4&=4\checkmark.\\\\
x+y&=5\\
3+2&\stackrel{?}{=}5\\
5&\stackrel{?}{=}5\checkmark.
\end{align*}$$
We got that the point $(3,2)$ verifies both equations, therefore it is the solution of the system.
