Question

solve the following system of equations graphically on the set of axes below.
$y = 3x - 8$
$y = -2x - 3$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \( 3x - 8=-2x - 3 \).
Add \( 2x \) to both sides: \( 3x + 2x-8=-3 \), so \( 5x-8=-3 \).
Add 8 to both sides: \( 5x=-3 + 8=5 \).
Divide by 5: \( x = 1 \).
Substitute \( x = 1 \) into \( y = 3x-8 \): \( y=3(1)-8=-5 \).

Step2: Graphical verification (concept)

For \( y = 3x - 8 \), when \( x = 0 \), \( y=-8 \); when \( x = 3 \), \( y=1 \). Plot these points.
For \( y=-2x - 3 \), when \( x = 0 \), \( y=-3 \); when \( x=-1 \), \( y=-1 \). Plot these points.
The lines intersect at \( (1, -5) \).

Answer:

The solution is \( x = 1 \), \( y=-5 \) (or the point \( (1, -5) \)).