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Find the solution to the following simultaneous equations:
x + 2y = 6
4x + 12y = 18
Correct Answer: A
Solve by isolating x in the first equation and substituting it into the second equation.
  1. Solving simultaneous equations involve reducing the number of unknowns by using one of the equations and substituting it into the other equation to solve for one of the unknown variables. Once x or y is determined, then use the other equation to solve for the other variable. Be aware that you may have a situation of an infinite or zero number of solutions.
  2. Take x + 2y = 6 and multiply each side of the equation by 4:
    4(x + 2y) = 4(6)
    This gives the equation 4x + 8y = 24
  3. We now have two equations:
    4x + 8y = 24
    4x + 12y = 18
  4. Subtract the lower from the upper equation. This gives the result:
    -4y = 6 or y = - 6 / 4 or y=-1.5
  5. Take y = -1.5 into either the lower or upper equation (here we use the upper equation):
    4x + 8(-1.5) = 24
    4x + -12 = 24
    4x = 36
    x = 9
  6. The answer is x = 9 and y = -1.5 which is the unique solution.

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