Question

The graph below represents the system of equations 3x+4y=12 and 2x-y=8.

A coordinate grid with 2 lines. One line passes through (0, 3) and (4, 0). The other line passes through (2, negative 4) and (4, 0).

Which ordered pair is a solution to the system of equations?

(0, 3)
(3, 0)
(4, 0)
(0, 4)

Answer 1

To find the solution to the system of equations represented by the two lines, we need to identify which of the given ordered pairs (0, 3), (3, 0), (4, 0), or (0, 4) lies at the intersection of the two lines. Since you mentioned the lines correspond to the equations \(3x + 4y = 12\) and \(2x - y = 8\), we can test each point in both equations to see which one satisfies both.

1. **For (0, 3)**:
- \(3(0) + 4(3) = 0 + 12 = 12\) (satisfies the first equation)
- \(2(0) - 3 = -3 \neq 8\) (does not satisfy the second equation)

2. **For (3, 0)**:
- \(3(3) + 4(0) = 9 + 0 = 9 \neq 12\) (does not satisfy the first equation)
- \(2(3) - 0 = 6 \neq 8\) (does not satisfy the second equation)

3. **For (4, 0)**:
- \(3(4) + 4(0) = 12 + 0 = 12\) (satisfies the first equation)
- \(2(4) - 0 = 8\) (satisfies the second equation)

4. **For (0, 4)**:
- \(3(0) + 4(4) = 0 + 16 = 16 \neq 12\) (does not satisfy the first equation)
- \(2(0) - 4 = -4 \neq 8\) (does not satisfy the second equation)

The only ordered pair that satisfies both equations in the system is **(4, 0)**. So, the solution to the system of equations is (4, 0).