solve the system by the elimination method:
3x-2y=2
2x+4y=-5
If you multiply the top equation by 2, you have
6x-4y=4
2x+4y=-5
now, if you add the two equations, see what happens.
To solve the system of equations using the elimination method, we need to eliminate one variable by adding the two equations together or subtracting one equation from the other.
First, let's eliminate the variable "x" by multiplying the first equation by 2 and the second equation by 3 to make the coefficients of "x" in both equations the same:
2(3x - 2y) = 2(2)
3(2x + 4y) = 3(-5)
Simplifying these equations, we get:
6x - 4y = 4
6x + 12y = -15
Now, we can subtract these two equations to eliminate "x":
(6x - 4y) - (6x + 12y) = 4 - (-15)
Simplifying the equation gives:
6x - 6x - 4y - 12y = 4 + 15
-16y = 19
Next, divide the equation by -16 to solve for "y":
-16y / -16 = 19 / -16
y = -19/16
Now, substitute the value of "y" (-19/16) back into either of the original equations. Let's use the first equation:
3x - 2(-19/16) = 2
Simplify the equation:
3x + 19/8 = 2
Move the constant term to the other side of the equation:
3x = 2 - 19/8
3x = 16/8 - 19/8
3x = -3/8
Finally, divide both sides of the equation by 3 to solve for "x":
(3x) / 3 = (-3/8) / 3
x = -1/8
Therefore, the solution to the system of equations is x = -1/8 and y = -19/16.