PSAT Math Grid-Ins Question 69: Answer and Explanation
Question: 69
Given 2x + 5y = 49 and 5x + 3y = 94, what is the product of x and y ?
Correct Answer: 51
Explanation:
51
Difficulty: Medium
Getting to the Answer: Rather than multiplying just one equation by a factor, you'll need to multiply both by a factor to use combination. Suppose you want to eliminate x. The coefficients of the x terms are 2 and 5, so you need to multiply the equations by numbers that will give you -10 and 10 as your new x term coefficients. To do this, multiply the first equation by -5 and the second equation by 2:
-5(2x + 5y = 49)
2(5x + 3y = 94)
Add the resulting equations:
Solving for y gives you 3. Next, plug 3 back in for y in either equation and solve for x, which equals 17. Multiplying x and y together yields 51. Grid in 51.
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