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Solve the system using elimination.
5x + 4y = 123x – 3y = 18
To solve this system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the two equations.
The given equations are:
1) 5x + 4y = 12
2) 3x - 3y = 18
First, let's make the coefficients of one of the variables the same by multiplying the second equation by 4 to match the coefficients of y:
1) 5x + 4y = 12
2) 12x - 12y = 72
Now, we can add the two equations to eliminate y:
(5x + 4y) + (12x - 12y) = 12 + 72
17x - 8y = 84
Now we have eliminated y and have a new equation in terms of x:
17x - 8y = 84
Now we can solve for x:
17x - 8y = 84
17x - 8(12) = 84
17x - 96 = 84
17x = 180
x = 180 / 17
x ≈ 10.59
Now that we have found x, we can substitute it back into one of the original equations to solve for y.
Using equation 1:
5x + 4y = 12
5(10.59) + 4y = 12
52.95 + 4y = 12
4y = 12 - 52.95
4y = -40.95
y = -40.95 / 4
y ≈ -10.24
Therefore, the solution to the system of equations is x ≈ 10.59 and y ≈ -10.24.