Solve the systems of equations by elimination
2x+4y = -8
3x-5y =21
To solve this system of equations by elimination, we will multiply one or both equations by a constant so that the coefficient of one of the variables will be the same in both equations when added or subtracted.
Let's start by multiplying the first equation by 5 and the second equation by 4 to eliminate the y variable:
5(2x+4y) = 5(-8)
4(3x-5y) = 4(21)
This simplifies to:
10x + 20y = -40
12x - 20y = 84
Now we can add these two equations together to eliminate the y variable:
(10x + 20y) + (12x - 20y) = -40 + 84
This simplifies to:
22x = 44
Divide both sides of the equation by 22 to solve for x:
22x/22 = 44/22
x = 2
Now we can substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:
2(2) + 4y = -8
4 + 4y = -8
4y = -12
y = -3
Therefore, the solution to the system of equations is x = 2 and y = -3.