Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{5}x - 8$
$y = -\frac{4}{5}x - 3$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \(\frac{1}{5}x - 8=-\frac{4}{5}x - 3\).
Add \(\frac{4}{5}x\) to both sides: \(\frac{1}{5}x+\frac{4}{5}x - 8=-\frac{4}{5}x+\frac{4}{5}x - 3\), which simplifies to \(x - 8=- 3\).
Add 8 to both sides: \(x - 8 + 8=-3 + 8\), so \(x = 5\).

Step2: Substitute x into one equation

Substitute \(x = 5\) into \(y=\frac{1}{5}x - 8\): \(y=\frac{1}{5}\times5 - 8=1 - 8=-7\).

Answer:

The solution is \((5, -7)\) (the point of intersection of the two lines). To graph:

• For \(y=\frac{1}{5}x - 8\), when \(x = 0\), \(y=-8\); when \(x = 5\), \(y=-7\). Plot \((0, -8)\) and \((5, -7)\) and draw the line.
• For \(y=-\frac{4}{5}x - 3\), when \(x = 0\), \(y=-3\); when \(x = 5\), \(y=-7\). Plot \((0, -3)\) and \((5, -7)\) and draw the line.