A system of equations is given.
Equation 1: 4x + 3y = 20
Equation 2: 3x + 2y = 12
Explain how to eliminate x in the system of equations.
To eliminate x in the system of equations, we need to use the method of elimination by multiplying one or both equations by a constant to make the coefficients of x equal or opposite. In this case, we can eliminate x by multiplying equation 1 by -3 and equation 2 by 4, which will give us opposite coefficients of x:
-3(4x + 3y = 20) = -12x - 9y = -60
4(3x + 2y = 12) = 12x + 8y = 48
Now we have two equations with opposite coefficients of x, so when we add them together, we can eliminate x:
-12x - 9y = -60
+ 12x + 8y = 48
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- y = -12
Simplifying the resulting equation gives us the value of y, and we can substitute it back into one of the original equations to solve for x:
4x + 3(-12) = 20
4x - 36 = 20
4x = 56
x = 14
Therefore, the solution to the system of equations is x = 14 and y = -12.