Question

Graph the system of equations to find the solution. You must show ALL work to earn full credit.

y=-4x-3
y=x+7
make it easy so I can copy and paste

Answer 1

To graph the system of equations and find the solution, follow these steps:

1. **Identify the equations**:

\[
\text{Equation 1: } y = -4x - 3
\]

\[
\text{Equation 2: } y = x + 7
\]

2. **Create a table of values for each equation**:

For Equation 1: \( y = -4x - 3 \)

| \( x \) | \( y \) |
|---------|------------------|
| -2 | \( -4(-2) - 3 = 8 - 3 = 5 \) |
| -1 | \( -4(-1) - 3 = 4 - 3 = 1 \) |
| 0 | \( -4(0) - 3 = 0 - 3 = -3 \) |
| 1 | \( -4(1) - 3 = -4 - 3 = -7 \) |
| 2 | \( -4(2) - 3 = -8 - 3 = -11 \) |

For Equation 2: \( y = x + 7 \)

| \( x \) | \( y \) |
|---------|------------------|
| -2 | \( -2 + 7 = 5 \) |
| -1 | \( -1 + 7 = 6 \) |
| 0 | \( 0 + 7 = 7 \) |
| 1 | \( 1 + 7 = 8 \) |
| 2 | \( 2 + 7 = 9 \) |

3. **Plot the points on a graph**:

- For Equation 1:
- Points to plot are (-2, 5), (-1, 1), (0, -3), (1, -7), (2, -11)
- For Equation 2:
- Points to plot are (-2, 5), (-1, 6), (0, 7), (1, 8), (2, 9)

4. **Draw the lines**:

- Draw a line through the points for Equation 1.
- Draw a line through the points for Equation 2.

5. **Find the intersection**:

- From the tables, we can see that both equations yield the same value of \( y \) at the point (-2, 5). This means they intersect at this point.

6. **Conclusion**:

The solution to the system of equations, where the two lines intersect, is:

\[
(x, y) = (-2, 5)
\]

### Summary

To find the solution graphically:

- **Equation 1:** \( y = -4x - 3 \)
- **Equation 2:** \( y = x + 7 \)
- **Point of Intersection:** \( (-2, 5) \) is the solution to the system of equations.

This point can be verified by substituting \( x = -2 \) into both equations, confirming they yield the same \( y \) value.