GMAT Equations
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GMAT Math - Equations Review
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EQUATIONS
In Algebra, you solve an equation for, say, y by isolating y on one side of the equality symbol. On the GMAT, however, you are often asked to solve for an entire term, say, 3 - y by isolating it on one side.
Example: If a + 3a is 4 less than b + 3b, then a - b =
(A) -4 (B) -1 (C) 1/5 (D) 1/3 (E) 2
Translating the sentence into an equation gives a + 3a = b + 3b - 4
Combining like terms gives 4a = 4b - 4
Subtracting 4b from both sides gives 4a - 4b = -4
Finally, dividing by 4 gives a - b = -1 Hence, the answer is (B).
Often on the GMAT, you can solve a system of two equations in two unknowns by merely adding or subtracting the equations--instead of solving for one of the variables and then substituting it into the other equation.
Example: If 4x + y = 14 and 3x + 2y = 13, then x - y =
Solution: Merely subtract the second equation from the first:
4x + y = 14
(-) 3x + 2y = 13
x - y = 1
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 of 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 in 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
4) Substitute the result in 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).