AlgebraVery hardConstant from a known intersection
Algebra practice question
In the xy-plane, the lines 3x + 2y = 12 and kx − 4y = 8, where k is a constant, intersect at a point whose x-coordinate is 2. What is the value of k?
Answer: 10
At x = 2 on the first line: 6 + 2y = 12, so y = 3. The point (2, 3) is on the second line too: 2k − 12 = 8, so 2k = 20 and k = 10.
Common wrong answers
- If you answered 3
- 3 is the y-coordinate of the intersection, not k.
- If you answered 4
- 4 is k with y = 0 (2k = 8), but the point's y-coordinate is 3, not 0.
- If you answered -2
- −2 comes from 2k + 12 = 8, adding 4y instead of subtracting it.
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