SAT Math Multiple Choice Question 810: Answer and Explanation

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Question: 810

15. If the ordered pair (x, y) satisfies the system of equations above, what is the sum of the values of x and y?

  • A.
  • B.
  • C.
  • D.

Correct Answer: D



Difficulty: Hard

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: When a system of equations involves lots of fractions, multiply each equation by its least common denominator to clear the fractions.

Getting to the Answer: Multiply the first equation by 8 and the second equation by 6 to clear the fractions:

Now, examine the new coefficients. Notice that multiplying the second equation by 7 (which yields 7x - 28y = 42) and adding the two equations will eliminate the y terms, leaving a single equation with one variable:

Substitute for x into the easier of the modified equations (the equations without the fractions), and solve for y:

The question asks for the sum of x and y, so add to get, which is (D).

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