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
- If x + y = 12 and x – y = –4, what is the value of y?
A. 10 B. –2 C. 8 D. 4 E. –11
- 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
- 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:
You can then solve for x.
Now that you know x is 4, you can put 4 in for x in either equation and determine the value of y:
The other choices can result from incorrect substitution, from miscalculation, or from both. Choice (D) is the value of x, not y.
- 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:
Now you have an equation with one variable, so it can be solved:
You now have the value of b, and you can put it in for b in either equation and solve for a:
Knowing the values of both a and b, you can put the values in for the variables in the expression 7a – (–8b):
