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Method of Substitution (Four-Step Method)

Although on the GMAT you can usually solve a system of two equations in two unknowns by merely adding or subtracting the equations, you still need to know a standard method for solving these types of systems.
 
The four-step method will be illustrated with the following system:
2x + y = 10
5x – 2y = 7
  1. Solve one of the equations for one of the variables:
    Solving the top equation for y yields y = 10 – 2x.
  2. Substitute the result from Step 1 into the other equation:
    Substituting y = 10 – 2x into the bottom equation yields 5x – 2(10 – 2x) = 7.
  3. Solve the resulting equation:
5x – 2(10 – 2x) = 7
5x – 20 + 4x = 7
9x – 20 = 7
9x = 27
x = 3
  1. Substitute the result from Step 3 into the equation derived in Step 1:
    Substituting x = 3 into y = 10 – 2x  yields y = 10 – 2(3) = 10 – 6 = 4.
Hence, the solution of the system of equations is the ordered pair (3, 4).




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