AlgebraHardTwo lines through the same point
Algebra practice question
In the xy-plane, the lines y = ax + 3 and y = 2x + b, where a and b are constants, both pass through the point (1, 5). What is the value of a + b?
Answer: 5
For the first line: 5 = a(1) + 3, so a = 2. For the second: 5 = 2(1) + b, so b = 3. a + b = 5.
Common wrong answers
- If you answered 2
- 2 is a alone.
- If you answered 3
- 3 is b alone.
- If you answered 8
- 8 is a + 3 + b with the 3 counted again; a = 2 and b = 3.
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