Question

solve the system by graphing. \

$$\begin{cases} y = 2x - 2 \\\\ y = -3x + 3 \\end{cases}$$

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

Explanation:

Step1: Find intersection by solving equations

Set \(2x - 2=-3x + 3\).
\(2x+3x = 3 + 2\)
\(5x=5\)

Step2: Solve for x

\(x=\frac{5}{5}=1\)

Step3: Substitute x into one equation

Substitute \(x = 1\) into \(y = 2x-2\):
\(y=2(1)-2=0\)

Answer:

The solution is \((1,0)\)