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.
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.