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 the two equations equal: $\frac{1}{5}x - 8 = -\frac{4}{5}x - 3$

Step2: Combine like terms

Add $\frac{4}{5}x$ to both sides: $\frac{1}{5}x + \frac{4}{5}x - 8 = -3$ → $x - 8 = -3$

Step3: Solve for x

Add 8 to both sides: $x = -3 + 8$ → $x = 5$

Step4: Substitute x into one equation

Use $y = \frac{1}{5}x - 8$: $y = \frac{1}{5}(5) - 8$ → $y = 1 - 8$ → $y = -7$

Answer:

The solution is $(5, -7)$ (the point where the two lines intersect when graphed).