Which is the solution for the system of equations x + 2y = 4 and -2x + y = 7

Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 4 and -2x + y = 7 ?

1. (-2, 3)
2. (-1, 2.5)
3. (1, 1.5)
4. (2, 1)
5. (4, 0)

Answer

The correct answer is A.

Solving the first equation for x gives

x = 4 - 2y

Plugging in the expression that x equals into the second equation gives

-2(4 - 2y) + y = 7

-8 + 4y + y = 7

5y = 15

y = 3

Now, take the value for y and plug it in for y in one of the original equations and solve for x,

x + 2(3) = 4

x + 6 = 4

x = -2

Therefore, (−2,3) is the solution for this system of equations.