Question

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Solve the system using elimination.

5x + 4y = 12
3x - 3y = 18

Answer 1

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.