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 \( (1, 5) \).