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

Answer 1

A)

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