solve the system by the elimination method 3x-2y=-9 -2x+4y=6
To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations by an appropriate number(s) so that the coefficients of one variable in both equations will be the same.
Let's start by multiplying the first equation by 2 to make the coefficient of y the same in both equations:
2(3x - 2y) = 2(-9)
6x - 4y = -18
Now we can rewrite the system as:
6x - 4y = -18
-2x + 4y = 6
Adding the two equations together, we can eliminate the y variable:
(6x - 4y) + (-2x + 4y) = -18 + 6
6x - 4y - 2x + 4y = -12
4x = -12
x = -12/4
x = -3
Substituting this value of x into the second equation to solve for y:
-2(-3) + 4y = 6
6 + 4y = 6
4y = 0
y = 0
Therefore, the solution to the system of equations is x = -3 and y = 0.