NECO 2005 Mathematics · Question 19

Find the value of 2a - b if a + b = 8 and 4a - b = 22

Options

A.2
B.4
C.6
D.8
E.10

Answer: E. 10

Explanation written with AI and checked against the answer key

Analyze the question: We have two equations with two unknowns, a and b, and we need the value of the expression 2a - b. Concept: Simultaneous equations can be solved by elimination. Adding or subtracting the equations removes one variable. Solution: Equation (1): a + b = 8 Equation (2): 4a - b = 22 Add the two equations (the b terms cancel): 5a = 30 a = 6 Substitute a = 6 into equation (1): 6 + b = 8 b = 2 Check in equation (2): 4(6) - 2 = 24 - 2 = 22 ✓ Now find 2a - b: 2a - b = 2(6) - 2 = 12 - 2 = 10 Answer: 10, which is option E. Tip: When the b terms have opposite signs (+b and -b), add the equations straight away. Always check your values in the other equation to avoid careless errors. Also read what the question asks for: it wants 2a - b, not a or b alone.

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