Solve the system using elimination.
5x + 4y = 12
3x – 3y = 18
To solve this system of equations using elimination, we need to multiply one or both equations by a constant such that the coefficients of either x or y will be equal when added or subtracted.
Let's start by multiplying the second equation by 4 to make the coefficient of y the same in both equations:
4(3x - 3y) = 4(18)
12x - 12y = 72
Now, our system of equations looks like this:
5x + 4y = 12
12x - 12y = 72
Next, we will add these two equations together to eliminate the y variable:
(5x + 4y) + (12x - 12y) = 12 + 72
5x + 12x + 4y - 12y = 84
17x - 8y = 84
Now we have a new equation with x and y coefficients. Let's solve for one variable in terms of the other:
17x - 8y = 84
17x = 8y + 84
x = (8y + 84) / 17
Now, we can substitute this expression for x back into one of the original equations so we can solve for y:
5x + 4y = 12
5((8y + 84) / 17) + 4y = 12
(40y + 420) / 17 + 4y = 12
40y + 420 + 4y * 17 = 204
40y + 420 + 68y = 204
108y + 420 = 204
108y = 204 - 420
108y = -216
y = -216 / 108
y = -2
Now that we have found y = -2, we can substitute this value into the equation we derived for x earlier:
x = (8(-2) + 84) / 17
x = (-16 +84) / 17
x = 68 / 17
x = 4
Therefore, the solution to the system of equations is x = 4, y = -2.