Question

Plug a few points into the original equations and check to show that each equation has one solution. Explain your work.

Answer 1

Let's consider the equations:

1) 2x + 3y = 7
2) 3x - 2y = 4

Let's plug in the point (x=1, y=1) into both equations:

For equation 1: 2(1) + 3(1) = 2 + 3 = 5 ≠ 7

For equation 2: 3(1) - 2(1) = 3 - 2 = 1 ≠ 4

Since the point (x=1, y=1) does not satisfy both equations simultaneously, it is not a solution for the system of equations. Therefore, it is not true that each equation has one solution.

Answer 2

Explain only with words without numbers

Answer 3

When plugging points into the original equations, we need to find a point that satisfies both equations simultaneously to show that each equation has one solution. If a point satisfies only one of the equations but not both, then it is not a solution for the system of equations. It is important to find a point that works for both equations to show that the system of equations has one solution.