Bryce took a quiz that consisted of true-or-false questions and multiple-choice questions. The true-or-false questions were worth 1 point each, and the multiple-choice questions were worth 2 points each. Bryce only knows that he answered 8 questions correctly and earned a total of 14 points. To determine the number of each type of question that he answered correctly, he wrote the system of linear equations x+y=8 and x+2y=14. Which ordered pair is a solution to this system of linear equations, and what does the ordered pair represent?
Answer
A
open paren 8 comma 0 close paren ; Bryce answered 8 true-or-false questions correctly and 0 multiple-choice questions correctly.
B
open paren 2 comma 6 close paren ; Bryce answered 2 true-or-false questions correctly and 6 multiple-choice questions correctly.
C
open paren 6 comma 2 close paren ; Bryce answered 6 true-or-false questions correctly and 2 multiple-choice questions correctly.
D
open paren 0 comma 8 close paren ; Bryce answered 0 true-or-false questions correctly and 8 multiple-choice questions correctly.
Explanation
Subtract x + y = 8 from x + 2y = 14 to get y = 6. Then x + 6 = 8, so x = 2. The ordered pair is (2, 6), where x is the number of true-or-false questions and y is the number of multiple-choice questions Bryce answered correctly. Thus, choice B is correct.
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