Question

Solve the systems of equations by elimination
2x+4y = -8
3x-5y =21

Answer 1

To solve the system of equations by elimination, we can eliminate one variable by multiplying one or both equations by appropriate factors so that the coefficients of one of the variables in both equations become opposites. Let's eliminate the variable "x" by multiplying the first equation by 3 and the second equation by 2:

(3)(2x+4y) = (3)(-8)
(2)(3x-5y) = (2)(21)

Simplifying these equations gives:

6x + 12y = -24
6x - 10y = 42

Now, subtracting the second equation from the first equation, we have:

(6x + 12y) - (6x - 10y) = -24 - 42
6x + 12y - 6x + 10y = -66
22y = -66
y = -66/22
y = -3

Substituting this value of y back into the first equation, we can solve for x:

2x + 4(-3) = -8
2x - 12 = -8
2x = -8 + 12
2x = 4
x = 4/2
x = 2

Therefore, the solution to the system of equations is x = 2 and y = -3.