AlgebraHardLine through the origin and a system's solution
Algebra practice question
The solution (x, y) to the system 2x − y = 2 and 4x + y = 16 lies on the line y = kx, where k is a constant. What is the value of k?
Answer: 4/3 or 1.333 or 1.33
Add the equations: 6x = 18, x = 3, and y = 2(3) − 2 = 4. The point (3, 4) is on y = kx when 4 = 3k, so k = 4/3.
Common wrong answers
- If you answered 7
- 7 is x + y, not the slope through the origin.
- If you answered 12
- 12 is xy.
- If you answered 3/4
- 3/4 is x/y, the reciprocal; k = y/x.
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