Answer
$\{(2,4)\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
y& =&3x&-2\\
y& = & -2x&+8
\end{matrix}\right.$
Graph the first equation :-
The given equation of the line is
$\Rightarrow y=3x-2$
The equation is in the slope-intercept form of a line
$y=mx+b$
Where, $y-$ intercept is $-2$, so the line passes through $A=(0,-2)$.
And slope $m=\frac{3}{1}=\frac{Rise}{Run}$
We plot the second point on the line by starting at $(0,-2)$; we move three units up (the rise) and one unit to the right (the run).
The second point is $B=(1,1)$.
Draw a straight line through these two points.
Graph the second equation :-
The given equation of the line is
$\Rightarrow y=-2x+8$
The equation is in the slope-intercept form of a line
$y=mx+b$
Where, $y-$ intercept is $8$, so the line passes through $C=(0,8)$.
And slope $m=\frac{-2}{1}=\frac{Rise}{Run}$
We plot the second point on the line by starting at $(0,8)$, We move two units down (the rise) and one unit to the right (the run).
The second point is $D=(1,6)$.
Draw a straight line through these two points.
The intersection point is the solution set.
We have intersection point $E=(2,4)$.
Hence, the solution set is $\{(x,y)\}=\{(2,4)\}$.
The graph is shown below.
