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 (solve equations)

Set \(2x - 2=-3x + 3\).
Add \(3x\) to both sides: \(2x+3x - 2=-3x+3x + 3\) → \(5x - 2 = 3\).
Add 2 to both sides: \(5x - 2+2 = 3+2\) → \(5x = 5\).
Divide by 5: \(x=\frac{5}{5}=1\).

Step2: Find y - value

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

Answer:

The solution is \((1,0)\) (the point where the two lines intersect when graphed).