WAEC 2013 Mathematics · Question 33

If $\frac{1}{2}$ x + 2y = 3 and $\frac{3}{2}$ x - 2y = 1, find (x + y)

Options

Answer: A. 3

Explanation written with AI and checked against the answer key

Analyze the question: We have two simultaneous equations in x and y, and we need the value of x + y (not x and y separately). Concept: Use the elimination method. The y-terms (+2y and −2y) cancel when we add the equations. Solution: Equation 1: ½x + 2y = 3 Equation 2: (3/2)x − 2y = 1 Add them: (½x + 3/2 x) + (2y − 2y) = 3 + 1 2x = 4 x = 2 Substitute x = 2 into Equation 1: ½(2) + 2y = 3 1 + 2y = 3 2y = 2 y = 1 Check in Equation 2: (3/2)(2) − 2(1) = 3 − 2 = 1 ✓ So x + y = 2 + 1 = 3. Answer: x + y = 3, which is option A. Tip: When two equations have the same coefficient of one variable with opposite signs (like +2y and −2y), just add them to eliminate it. Also, always check your answer in the second equation to be sure.

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If 12\frac{1}{2}21​x + 2y = 3 and 32\frac{3}{2}23​x - 2y = 1, find (x + y)

Options

Answer: A. 3

If $\frac{1}{2}$ x + 2y = 3 and $\frac{3}{2}$ x - 2y = 1, find (x + y)