To eliminate x in the system of equations, we need to make the coefficients of x in both equations equal to each other or multiples of each other. In this case, we can achieve this by multiplying Equation 1 by 3 and Equation 2 by 4.
Multiplying Equation 1 by 3:
3(4x + 3y) = 3(20)
12x + 9y = 60
Multiplying Equation 2 by 4:
4(3x + 2y) = 4(12)
12x + 8y = 48
Now, we have two equations:
Equation 3: 12x + 9y = 60
Equation 4: 12x + 8y = 48
Subtracting Equation 4 from Equation 3 to eliminate x:
(12x + 9y) - (12x + 8y) = 60 - 48
12x - 12x + 9y - 8y = 12
y = 12
Now that we have found the value of y, we can substitute y = 12 back into one of the original equations (Equation 1 or Equation 2) to solve for x.
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.
1 answer