Solve the system of equations using the addition method: x + 2y = 6
2x - 3y = -16
A) $x = 14 , y = - 4$
B) $x = 0 , y = 5 \frac { 1 } { 3 }$
C) $x = - 2 , y = 4$
D) $x = - 2 , y = 2$

Question

Quizplus · Accepted Answer

To use the addition method we need to eliminate a variable by adding the equations. We want to eliminate x so we multiple the first equation by -2.

-2(x + 2y = 6) = -2x - 4y = -12

Now we can add the two equations.

-2x - 4y = -12
2x - 3y = -16
___________
-7y = -28

Solving for y we get y = 4. Now we can substitute y = 4 into either equation to solve for x. Plugging into the first equation we get:

x + 2(4) = 6
x + 8 = 6
x = -2

Therefore, the solution is (x,y) = (-2,4). This matches choice C.

Solve the System of Equations Using the Addition Method: X x=14,y=−4x = 14 , y = - 4x=14,y=−4

Solve the System of Equations Using the Addition Method: X $x = 14 , y = - 4$