ASVAB Mathematics Knowledge Practice: Systems of Equations - dummies

ASVAB Mathematics Knowledge Practice: Systems of Equations

By Consumer Dummies

The Mathematics Knowledge subtest on the ASVAB will throw one or two problems at you that involve systems of equations. As you’ll see in the following practice questions, they may look a little difficult, but you can solve them using either the elimination or substitution method.

Practice questions

  1. Solve:

    ASVAB_1101

    A. (3, 4)
    B. (4, 3)
    C. (–3, 4)
    D. (–3, –4)

  2. Solve the system:

    ASVAB_1102

    A. x = 5 and y = 1
    B. x = 4 and y = 1
    C. x = 4 and y = 2
    D. x = 5 and y = 2

Answers and explanations

  1. The correct answer is Choice (C).

    Solve this system by using the elimination method. Multiply each factor in the second equation by –1 and then add the equations:

    ASVAB_1103

    The solution is –2y = –8, which you can solve normally:

    ASVAB_1104

    Put y into the simplest equation (although either equation will work) to solve for x:

    ASVAB_1105

    Express your answer as (x, y). In this case, the answer is (–3, 4).

  2. The correct answer is Choice (B).

    When you solve a system, it’s given that x is the same in both equations; so is y.

    One approach is to isolate one variable in one equation by solving xy = 3:

    ASVAB_1106

    Replace x in the first equation with 3 + y:

    ASVAB_1107

    Because y = 1, you can substitute 1 for y in the original equation to find x:

    ASVAB_1108