WAEC 2016 Mathematics · Question 45

Given that 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?

Options

A.1
B.3
C.7
D.17

Answer: C. 7

Explanation written with AI and checked against the answer key

Analyze the question: We have two simultaneous equations. We must find x, then work out how much 7x exceeds 10, which is 7x − 10. Concept: Use elimination to solve simultaneous equations. Solution: Equation 1: 2x + y = 7 Equation 2: 3x − 2y = 3 Multiply Equation 1 by 2 so the y terms cancel: 4x + 2y = 14 Add this to Equation 2: 4x + 2y + 3x − 2y = 14 + 3 7x = 17 So 7x = 17. (Check: x = 17/7, y = 7 − 34/7 = 15/7. Then 3x − 2y = 51/7 − 30/7 = 21/7 = 3 ✓) Now, by how much is 7x greater than 10? 7x − 10 = 17 − 10 = 7 Answer: 7x exceeds 10 by 7, which is option C. Tip: When a question asks for an expression such as 7x, check whether elimination gives it directly. Here, adding the equations after doubling the first gave 7x immediately, so you don't need to find x and y separately. This saves time in the exam.

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