Solve each system of equations by graphing.

$\begin{array}{c}3x+2y=12\\ x-2y=4\end{array}$

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Consider the first equation $3x+2y=12$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by $3x$and then divide by 2.

$\begin{array}{c}3x+2y-3x=12-3x\\ 2y=12-3x\\ y=\frac{12}{2}-\frac{3}{2}x\\ y=-\frac{3}{2}x+6\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $-\frac{3}{2}$ and intercept of y-axis c is $6$.

Now, consider the second equation $x-2y=4$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by $x$and then divide by $-2$.

$\begin{array}{c}x-2y-x=4-x\\ -2y=-x+4\\ y=\frac{1}{2}x-2\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $\frac{1}{2}$ and intercept of y-axis c is $-2$.

Plot the equations on the same plane and the point where both the equations intersect is the solution of the system of the equations.

The red line denotes the equation $3x+2y=12$ and blue line denotes the equation $x-2y=4$.

Therefore, the point of intersection is $\left(4,0\right)$.

The point of intersection is solution of system of equations if the point satisfies both the equation.

Substitute the point $\left(4,0\right)$in the equation $3x+2y=12$.

Substitute x as 4 and y as 0 and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}3\left(4\right)+2\left(0\right)=12\\ 12+0=12\\ 12=12\end{array}$

Since, this is true so the point $\left(4,0\right)$satisfy the equation $3x+2y=12$.

Substitute the point $\left(4,0\right)$in the equation $x-2y=4$.

Substitute x as 4 and y as 0 and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}4-2\left(0\right)=4\\ 4-0=4\\ 4=4\end{array}$

Since, this is true so the point $\left(4,0\right)$ satisfy the equation $x-2y=4$.

Hence, the solution of the system of equations is $\left(4,0\right)$.