Equation A: 3x + y = 23

Equation B: 4x - y = 12
what are the system of equations to determine which of the following statements are true. Select all that apply.

1 answer

To determine which of the following statements are true, we need to solve the system of equations:

Equation A: 3x + y = 23
Equation B: 4x - y = 12

1. The point (5, 8) is a solution to the system of equations.

Let's substitute the values of x = 5 and y = 8 into both equations and check if they are satisfied.

For Equation A: 3(5) + 8 = 15 + 8 = 23, which is true.

For Equation B: 4(5) - 8 = 20 - 8 = 12, which is true.

Since both equations are true with the values x = 5 and y = 8, the point (5, 8) is indeed a solution to the system of equations.

2. The point (3, 7) is a solution to the system of equations.

Let's substitute the values of x = 3 and y = 7 into both equations and check if they are satisfied.

For Equation A: 3(3) + 7 = 9 + 7 = 16, which is not equal to 23.

For Equation B: 4(3) - 7 = 12 - 7 = 5, which is not equal to 12.

Since at least one of the equations is not true with the values x = 3 and y = 7, the point (3, 7) is not a solution to the system of equations.

Therefore, the only true statement is:

1. The point (5, 8) is a solution to the system of equations.