Plug more than one point into the original equations, and check to show that the equations can have more than one solution. Explain your work.

Answer 1

Let's consider the system of equations:

1) x + y = 5
2) 2x - y = 1

We will plug in two different points into the equations and show that they satisfy both equations.

Point 1: x = 2, y = 3
1) 2 + 3 = 5 (satisfies equation 1)
2) 2(2) - 3 = 4 - 3 = 1 (satisfies equation 2)

Therefore, the point (2, 3) is a solution to the system of equations.

Point 2: x = 1, y = 4
1) 1 + 4 = 5 (satisfies equation 1)
2) 2(1) - 4 = 2 - 4 = -2 (does not satisfy equation 2)

Therefore, the point (1, 4) is not a solution to the system of equations.

From this, we can see that the system of equations can have more than one solution, as shown by the different points that satisfy both equations.