Solve each system of equations by graphing.

$\begin{array}{c}\text{5}x-11=4y\\ 7x-1=8y\end{array}$

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 $5x-11=4y$.

Rewrite the equation in form of slope-intercept form.

Divide both sides by 4 and rearrange the terms.

$\begin{array}{c}\frac{5x-11}{4}=\frac{4y}{4}\\ \frac{5}{4}x-\frac{11}{4}=y\\ y=\frac{5}{4}x-\frac{11}{4}\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $\frac{5}{74}$ and intercept of y-axis c is $-\frac{11}{4}$.

Now, consider the second equation $7x-1=8y$.

Rewrite the equation in form of slope-intercept form.

Divide both sides by 8 and rearrange the terms.

$\begin{array}{c}\frac{7x-1}{8}=\frac{8y}{8}\\ \frac{7}{8}x-\frac{1}{8}=y\\ y=\frac{7}{8}x-\frac{1}{8}\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $\frac{7}{8}$ and intercept of y-axis c is $-\frac{1}{8}$.

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 $5x-11=4y$ and blue line denotes the equation $7x-1=8y$.

Therefore, the point of intersection is $\left(7,6\right)$.

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

Substitute the point $\left(7,6\right)$in the equation $5x-11=4y$.

Substitute x as 5 and y as 6 and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}5\left(7\right)-11=4\left(6\right)\\ 35-11=24\\ 24=24\end{array}$

Since, this is true so the point $\left(7,6\right)$ satisfy the equation $5x-11=4y$.

Substitute the point $\left(7,6\right)$ in the equation $7x-1=8y$.

Substitute x as 5 and y as $6$ and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}7\left(7\right)-1=8\left(6\right)\\ 49-1=48\\ 48=48\end{array}$

Since, this is true so the point $\left(7,6\right)$ satisfy the equation $7x-1=8y$.

Hence, the solution of the system of equations is $\left(7,6\right)$.