At what point do the lines 2x + y = 7 and x - y = 2 intersect?
Answer and explanation
Correct answer: A. (3, 1)
- Step 1: Adding both equations eliminates y: (2x + y) + (x - y) = 7 + 2 => 3x = 9 => x = 3. Step 2. Substitute x = 3 into x - y = 2 => 3 - y = 2 => y = 1. Intersecting point is (3, 1). Answer: (3, 1). Why not the others: (1, 5) satisfies only the first line; (4, 2) satisfies x - y = 2 but 2(4)+2 = 10 != 7; (2, 3) satisfies 2(2)+3=7 but 2-3 = -1 != 2.
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