Question

Which point on the graph is the solution to the system equations? Explain how you know. (2 points)'

1. (0,6)

2. (-1,4)

3. (-5,0)

Answer 1

To determine which point on the graph is the solution to the system of equations, we must first plug in the x and y values into both equations and see if they satisfy both equations.

Let's use the system of equations:

- Equation 1: 2x + 3y = 6
- Equation 2: x + y = 4

1. For point (0,6):
- Equation 1: 2(0) + 3(6) = 6 which simplifies to 18 = 6 (FALSE)
- Equation 2: 0 + 6 = 4 (FALSE)

2. For point (-1,4):
- Equation 1: 2(-1) + 3(4) = 6 which simplifies to 8 = 6 (FALSE)
- Equation 2: -1 + 4 = 4 which simplifies to 3 = 4 (FALSE)

3. For point (-5,0):
- Equation 1: 2(-5) + 3(0) = 6 which simplifies to -10 = 6 (FALSE)
- Equation 2: -5 + 0 = 4 (FALSE)

None of the points (0,6), (-1,4), and (-5,0) satisfy both equations. Therefore, there is no solution among these points on the graph.