Solve each system of equations by graphing.

$\begin{array}{c}y=3x-8\\ y=x-8\end{array}$

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 $y=3x-8$.

Rewrite the equation in form of slope-intercept form.

$y=3x+\left(-8\right)$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is 3 and intercept of y-axis c is $-8$.

Now, consider the second equation $y=x-8$.

Rewrite the equation in form of slope-intercept form.

$y=x+\left(-8\right)$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $1$ and intercept of y-axis c is $-8$.

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 $y=3x-8$ and blue line denotes the equation $y=x-8$.

Therefore, the point of intersection is $\left(0,-8\right)$.

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

Substitute the point $\left(0,-8\right)$ in the equation $y=3x-8$.

Substitute x as 0 and y as $-8$ and check whether right hand side is equal to left hand side of the equation.

Since, this is true so the point $\left(0,-8\right)$ satisfy the equation $y=3x-8$.

Substitute the point $\left(1,-2\right)$ in the equation $y=-3x+1$.

Substitute x as 0 and y as $-8$ and check whether right hand side is equal to left hand side of the equation.

Since, this is true so the point $\left(0,-8\right)$ satisfy the equation $y=x-8$.

Hence, the solution of the system of equations is $\left(0,-8\right)$.