To solve the system using elimination, we need to eliminate one variable by adding or subtracting the two equations.
First, let's multiply the second equation by 4 to make the coefficients of y the same in both equations:
4(3x - 3y) = 4(18)
12x - 12y = 72
Now the system becomes:
5x + 4y = 12
12x - 12y = 72
Next, let's add the two equations together to eliminate y:
(5x + 4y) + (12x - 12y) = 12 + 72
5x + 12x + 4y - 12y = 84
17x - 8y = 84
Now we have a new equation: 17x - 8y = 84.
Let's rearrange this equation to solve for x:
17x = 8y + 84
x = (8y + 84)/17
Now we substitute this value of x into one of the original equations, let's use the first equation:
5( (8y + 84)/17 ) + 4y = 12
Now we solve for y:
(40y + 420)/17 + 4y = 12
(40y + 420) + 68y = 12*17
40y + 420 + 68y = 204
108y + 420 = 204
108y = 204 - 420
108y = -216
y = -216/108
y = -2
Now we substitute this value of y back into the equation we found for x:
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.
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Solve the system using elimination.
5x + 4y = 12
3x - 3y = 18
1 answer