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 (algebraically, then plot)

Set \(3x - 8=-2x - 3\).
Add \(2x\) to both sides: \(5x - 8=-3\).
Add \(8\) to both sides: \(5x = 5\).
Divide by \(5\): \(x = 1\).

Substitute \(x = 1\) into \(y = 3x - 8\): \(y=3(1)-8=-5\).

Step2: Plot \(y = 3x - 8\)

• When \(x = 0\), \(y=-8\) (point \((0, -8)\)).
• When \(x = 2\), \(y=3(2)-8=-2\) (point \((2, -2)\)).

Step3: Plot \(y=-2x - 3\)

• When \(x = 0\), \(y=-3\) (point \((0, -3)\)).
• When \(x = 1\), \(y=-2(1)-3=-5\) (point \((1, -5)\)).

Answer:

The solution (intersection point) is \((1, -5)\). To graph:

• For \(y = 3x - 8\), plot \((0, -8)\) and \((2, -2)\), draw a line.
• For \(y=-2x - 3\), plot \((0, -3)\) and \((1, -5)\), draw a line.

The lines intersect at \((1, -5)\).