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