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What is the solution to the following system of equations for X and Y?
2X + 3Y = 17
X + 2Y = 10
Correct Answer: D
Multiply the second equation by 2
  1. The solution to this problem begins with the recognition that equations are discrete entities. This means that we may perform some operations on equations without altering their validity.
  2. In this instance, the examinee should (1) change the places of the two equations, (2) multiply what is now the first equation by two, (3) subtract the second equation from the first, solving for the remaining variable. (4) This permits a simple substitution for the solution of the second variable. This is much easier to do than to read, as the steps detailed below should make clear.
  3. 1- X + 2Y = 10
    2X + 3Y = 17

    2[X + 2Y = 10] = 2X + 4Y = 20

    2X + 4Y = 20
    -2X - 3Y = -17
    0 + Y = 3

    X + 2Y = X + 2(3) = X + 6 = 10
    X + 6 - 6 = 10 - 6
    X = 4
  4. We thus arrive at the conclusion that (4,3) makes both equations true.
  5. This could be double-checked by plugging x = 4 and y = 3 into both equations.

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