Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{2}{3}x - 7$
$y = -\frac{1}{3}x - 4$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step 1: Analyze the first equation \( y = \frac{2}{3}x - 7 \)

To graph this line, we can find two points.

• When \( x = 0 \), \( y = \frac{2}{3}(0) - 7 = -7 \). So one point is \( (0, -7) \).
• When \( x = 3 \), \( y = \frac{2}{3}(3) - 7 = 2 - 7 = -5 \). So another point is \( (3, -5) \).

Step 2: Analyze the second equation \( y = -\frac{1}{3}x - 4 \)

To graph this line, we find two points.

• When \( x = 0 \), \( y = -\frac{1}{3}(0) - 4 = -4 \). So one point is \( (0, -4) \).
• When \( x = 3 \), \( y = -\frac{1}{3}(3) - 4 = -1 - 4 = -5 \). So another point is \( (3, -5) \).

Step 3: Find the intersection point

The two lines intersect where they have the same \( x \) and \( y \) values. From the points we calculated, both lines pass through \( (3, -5) \). This is the solution to the system of equations.

Answer:

The solution to the system of equations is \( x = 3 \), \( y = -5 \) (or the point \((3, -5)\)).