Question

What is the solution to the system of equations y = 6x - 1 and y = 3x + 2? Complete the table to support your answer. (6 points) x values y = 6x - 1 y = 3x + 2 -1 0 1 2 3

Answer 1

To find the solution to the system of equations \( y = 6x - 1 \) and \( y = 3x + 2 \), we can compute the values of \( y \) for the given \( x \) values in each equation. Then we'll compare the results to find the point where the two equations intersect.

### Calculate \( y \) for different \( x \) values

#### For the equation \( y = 6x - 1 \):
- \( x = -1 \): \( y = 6(-1) - 1 = -6 - 1 = -7 \)
- \( x = 0 \): \( y = 6(0) - 1 = 0 - 1 = -1 \)
- \( x = 1 \): \( y = 6(1) - 1 = 6 - 1 = 5 \)
- \( x = 2 \): \( y = 6(2) - 1 = 12 - 1 = 11 \)
- \( x = 3 \): \( y = 6(3) - 1 = 18 - 1 = 17 \)

#### For the equation \( y = 3x + 2 \):
- \( x = -1 \): \( y = 3(-1) + 2 = -3 + 2 = -1 \)
- \( x = 0 \): \( y = 3(0) + 2 = 0 + 2 = 2 \)
- \( x = 1 \): \( y = 3(1) + 2 = 3 + 2 = 5 \)
- \( x = 2 \): \( y = 3(2) + 2 = 6 + 2 = 8 \)
- \( x = 3 \): \( y = 3(3) + 2 = 9 + 2 = 11 \)

### Complete the table:

| \( x \) | \( y = 6x - 1 \) | \( y = 3x + 2 \) |
|-------|-------------------|-------------------|
| -1 | -7 | -1 |
| 0 | -1 | 2 |
| 1 | 5 | 5 |
| 2 | 11 | 8 |
| 3 | 17 | 11 |

### Find intersection point:
From the table, we can see that \( y \) is equal for \( x = 1 \):
- At \( x = 1 \), both equations yield \( y = 5 \).

### Solution:
The solution to the system of equations is \( (1, 5) \).