# 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

**Explanation:**

**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 7*x* - 28*y* = 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).