Question

1. solve the following system of equations graphically on the set of axes below and state the coordinates of the solution.

$y = \frac{2}{3}x - 4$ $y = -\frac{1}{3}x - 7$

Explanation:

Step1: Find intersection algebraically

Set equations equal:
$$\frac{2}{3}x - 4 = -\frac{1}{3}x - 7$$

Step2: Combine like terms

Add $\frac{1}{3}x$ to both sides:
$$\frac{2}{3}x + \frac{1}{3}x - 4 = -7$$
$$x - 4 = -7$$

Step3: Solve for x

Add 4 to both sides:
$$x = -7 + 4$$
$$x = -3$$

Step4: Find y with x=-3

Substitute into $y=\frac{2}{3}x - 4$:
$$y = \frac{2}{3}(-3) - 4$$
$$y = -2 - 4$$
$$y = -6$$

Step5: Verify graph points

For $y=\frac{2}{3}x - 4$:

• y-intercept: $(0, -4)$; when $x=3$, $y=-2$

For $y=-\frac{1}{3}x - 7$:

• y-intercept: $(0, -7)$; when $x=-3$, $y=-6$

Lines intersect at $(-3, -6)$

Answer:

The coordinates of the solution are $(-3, -6)$