Practice Math Questions for Praxis: Solving Algebraic Expressions Using Elimination - dummies

Practice Math Questions for Praxis: Solving Algebraic Expressions Using Elimination

By Carla Kirkland, Chan Cleveland

When you’re asked to solve a system of equations on the Praxis Core exam, start by checking the variables. If the variables in both equations have the same coefficients, then you can solve them using elimination.

In the first practice question, you’re given a pair of algebraic equations that you can solve with simple elimination. In the second question, you need to begin with some multiplication so that one set of coefficients has the same absolute value.

Practice questions

  1. If x + y = 12 and xy = –4, what is the value of y?

    A. 10
    B. –2
    C. 8
    D. 4
    E. –11

  2. If 10a + 2b = 14 and –5a – 7b = 11, what is the value of 7a – (–8b)?

    A. –10
    B. 22
    C. 6
    D. –3
    E. 14

Answers and explanations

  1. The correct answer is Choice (C).

    You can use the substitution method or elimination method to find the value of one variable and then substitute in that value to find the other variable’s value.

    With the elimination method, you can add the two equations and get an equation without y:

    PRAXIS_2001NEW

    You can then solve for x.

    PRAXIS_2002

    Now that you know x is 4, you can put 4 in for x in either equation and determine the value of y:

    PRAXIS_2003

    The other choices can result from incorrect substitution, from miscalculation, or from both. Choice (D) is the value of x, not y.

  2. The correct answer is Choice (A).

    In this case, elimination is the better method of solving the system of equations for most people because there’s no variable with a coefficient of 1 (which would make substitution ideal) and the second equation can be multiplied by 2 to make the a coefficients have the same absolute value (so you can eliminate the a‘s). Multiply the second equation by 2 and add the equations:

    PRAXIS_2004

    Now you have an equation with one variable, so it can be solved:

    PRAXIS_2005

    You now have the value of b, and you can put it in for b in either equation and solve for a:

    PRAXIS_2006

    Knowing the values of both a and b, you can put the values in for the variables in the expression 7a – (–8b):

    PRAXIS_2007