Question

Which system of equations has the solution (4,−2)?

A. {x+y=2
2x−y=10

B. {x−y=2
2x−y=10

C. {x+y=2
−3x+y=10

D. {x+y=2
2x+y=−10

1. hongcuc2
A)
Step-by-step explanation:
To find the answer we must solve each of the systems separately. Starting with the first one:
x + y = 2
2x – y = 10
We must find what x or y is equal to and then replace it in the second equation. I’ll go with y as it seems easier:
x + y = 2
y = 2 – x
Now that we found y we replace it in the second equation this way. Be careful with the signs, the minus with change our signs:
2x – (2 – x) = 10
2x – 2 + x = 10
3x = 12
x = 12/3
x = 4
Now that we have x, we replace the variable with its value in one of the equations. Again, for simplicity I’ll go with the one that seems easier.
4 + y = 2
y = 2 – 4
y = – 2