In the following practice questions, you start by performing a simple substitution within a rational algebraic expression; then, you go a little deeper by performing a more complex substitution to solve for two variables.
Practice questions
- If w = y, what is the value of
- If 2x + 4y = 32 and x – 2y = –12, which of the following is true?
A. x + y = 10 B. 5x – y = 3 C. 8x + y = 26 D. 3x – 2y = –11 E. x – y = –2
Answers and explanations
- The correct answer is Choice (D).
Because w and y have the same value, you can substitute one in for the other and work with only one variable, which allows for cancelations:
- The correct answer is Choice (B).
You can use elimination or substitution to solve for x or y. Substitution might be easier because in the second equation, you can easily isolate the x because it doesn't have a written coefficient (and neither variable has two coefficients with the same absolute value, which would be ideal for elimination). To use that method, solve the second equation for x in terms of y:
Next, substitute –12 + 2y in for x in the other equation, 2x + 4y = 32. You'll then be working with an equation with one variable, and an equation with one variable can be solved.
Now that you know y has a value of 7, you can put 7 in for y in either given equation to find x:
To check your answer, you can put 2 in for x and 7 in for y in the given equations and see that the pair makes both equations true. Next, test each of the choices to see which one is made true by the pair. The only one it works for is Choice (B).