Question

solve the system by graphing.\

$$\begin{cases}-4x + 3y = 24\\\\x + 3y = 9\\end{cases}$$

\dots\
use the graphing tool to graph the system.\
click to enlarge graph

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(-4x + 3y=24\), we solve for \(y\):
\(3y = 4x + 24\), then \(y=\frac{4}{3}x + 8\)
For the second equation \(x + 3y=9\), we solve for \(y\):
\(3y=-x + 9\), then \(y=-\frac{1}{3}x + 3\)

Step2: Find intersection point (solve the system algebraically to check)

Subtract the second equation from the first equation:
\((-4x + 3y)-(x + 3y)=24 - 9\)
\(-4x+3y - x - 3y=15\)
\(-5x=15\)
\(x=- 3\)

Substitute \(x = - 3\) into the second equation \(x + 3y=9\):
\(-3+3y=9\)
\(3y=9 + 3=12\)
\(y = 4\)

Answer:

The solution of the system is \(x=-3,y = 4\) or the ordered pair \((-3,4)\)