Question

solve the following system of equations graphically on the set of axes below.
$y = -2x - 1$
$y = \frac{1}{3}x + 6$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \(-2x - 1=\frac{1}{3}x + 6\). Multiply all terms by 3 to eliminate fraction: \(-6x - 3 = x + 18\).

Step2: Solve for x

Bring x terms to left and constants to right: \(-6x - x=18 + 3\), so \(-7x = 21\), then \(x=-3\).

Step3: Find y using x=-3

Substitute \(x = -3\) into \(y=-2x - 1\): \(y=-2(-3)-1 = 6 - 1 = 5\).

Answer:

The solution is \(x = -3\), \(y = 5\) (the point of intersection is \((-3, 5)\)).