Question

Solve the following system of equations graphically on the set of axes below.
y, equals, start fraction, 2, divided by, 3, end fraction, x, plus, 3
y= 2/3x + 3
y, equals, minus, start fraction, 4, divided by, 3, end fraction, x, minus, 3
y=− 4/3x − 3

Answer 1

To solve the system of equations graphically, we will plot both equations on the same set of axes and identify their intersection point.

### Step 1: Write the equations

1. \( y = \frac{2}{3}x + 3 \)
2. \( y = -\frac{4}{3}x - 3 \)

### Step 2: Identify Points to Plot

**For the first equation \( y = \frac{2}{3}x + 3 \)**:

- When \( x = 0 \):
\[
y = \frac{2}{3}(0) + 3 = 3
\]
Point: \( (0, 3) \)

- When \( x = 3 \):
\[
y = \frac{2}{3}(3) + 3 = 2 + 3 = 5
\]
Point: \( (3, 5) \)

- When \( x = -3 \):
\[
y = \frac{2}{3}(-3) + 3 = -2 + 3 = 1
\]
Point: \( (-3, 1) \)

**For the second equation \( y = -\frac{4}{3}x - 3 \)**:

- When \( x = 0 \):
\[
y = -\frac{4}{3}(0) - 3 = -3
\]
Point: \( (0, -3) \)

- When \( x = 3 \):
\[
y = -\frac{4}{3}(3) - 3 = -4 - 3 = -7
\]
Point: \( (3, -7) \)

- When \( x = -3 \):
\[
y = -\frac{4}{3}(-3) - 3 = 4 - 3 = 1
\]
Point: \( (-3, 1) \)

### Step 3: Plot the Points and Draw the Lines

1. **Plot the points for the first equation**:
- \( (0, 3) \)
- \( (3, 5) \)
- \( (-3, 1) \)

2. **Plot the points for the second equation**:
- \( (0, -3) \)
- \( (3, -7) \)
- \( (-3, 1) \)

3. **Draw the lines** through the respective points.

### Step 4: Identify the Intersection Point

From the calculations, you will notice that both equations pass through the point \( (-3, 1) \).

### Conclusion

The solution to the system of equations \( y = \frac{2}{3}x + 3 \) and \( y = -\frac{4}{3}x - 3 \) is:
\[
\boxed{(-3, 1)}
\]