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Solve the system using elimination.
5x + 4y = 12
3x – 3y = 18
To solve the system using elimination, we need to eliminate one variable by adding or subtracting the equations. In this case, we notice that if we multiply the second equation by 4, it will allow us to eliminate the y variable:
4(3x - 3y) = 4(18)
12x - 12y = 72
Now we can add this new equation to the first equation:
(5x + 4y) + (12x - 12y) = 12 + 72
5x + 12x + 4y - 12y = 84
17x - 8y = 84
Now we have a new equation:
17x - 8y = 84
We can solve this equation for one variable, for example, x:
17x = 84 + 8y
x = (84 + 8y) / 17
Now we substitute this expression for x in one of the original equations. Let's use the first equation:
5( (84 + 8y) / 17 ) + 4y = 12
We can simplify this equation by multiplying everything by 17 to clear the fraction:
5(84 + 8y) + 68y = 204
420 + 40y + 68y = 204
108y = 204 - 420
108y = -216
y = -216 / 108
y = -2
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
5x + 4(-2) = 12
5x - 8 = 12
5x = 12 + 8
5x = 20
x = 20 / 5
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -2.