Answer:
Systems A (x + y = 3 and 2x + y = 12) and D (2x + 2y = 4 and x - 4y = 12)
Explanation:
Background information:
- For any system of equations, the values are only solutions if and only if they make both equations true when their plugged into both equations in the equations.
- This means that if the solutions make one equation true, you still need to check the other equation.
- However, if the solutions make one equation true, this automatically means it they can't be the solutions since both equations must be true when plugging in the solutions.
A.
Checking x = 9 and y = -6 in x + y = 3:
9 - 6 = 3
3 = 3
Checking x = 9 and y = -6 in 2x + y = 12:
2(9) - 6 = 12
18 - 6 = 12
12 = 12
Thus, A is the first system of linear equations that is solved correctly.
B.
Checking x = 103 and y = 43 in 5x + y = 10:
5(103) + 43 = 10
515 + 43 = 10
558 = 10
Because the equation is not true, the system of equations is solved incorrectly.
C.
Checking x = 32 and y = 112 in x + y = 7:
32 + 112 = 7
144 = 7
Because the equation is not true, the system of equations is solved incorrectly.
D.
Checking x = 4 and y = -2 in 2x + 2y = 4:
2(4) + 2(-2) = 4
8 - 4 = 4
4 = 4
Checking x = 4 and y = -2 in x - 4y = 12:
4 - 4(-2) = 12
4 + 8 = 12
12 = 12
Thus, D is the second system of equations that is solved correctly.
E.
We don't have to check E since we're told that there are only two systems that are solved correctly.