Question

solve the following system of equations graphically on the set of axes below.
$y = -x + 4$
$y = 2x - 2$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \(-x + 4 = 2x - 2\).
Add \(x\) to both sides: \(4 = 3x - 2\).
Add 2 to both sides: \(6 = 3x\).
Divide by 3: \(x = 2\).

Step2: Find y - value

Substitute \(x = 2\) into \(y=-x + 4\): \(y=-2 + 4 = 2\).

Answer:

The solution is \(x = 2\), \(y = 2\) (the point \((2, 2)\) is the intersection of the two lines).