AlgebraVery hardConstant for a consistent dependent system
Algebra practice question
A system consists of the equations 2x + 3y = 7 and 4x + 6y = c, where c is a constant. If the system has at least one solution, what must the value of c be?
Answer: 14
The left side 4x + 6y is exactly 2 times 2x + 3y. So if 2x + 3y = 7, then 4x + 6y = 14. Any other value of c makes the lines parallel with no solution; c = 14 makes them the same line.
Common wrong answers
- If you answered 7
- With c = 7, the second equation says 2x + 3y = 3.5, contradicting the first: no solution.
- If you answered 28
- 28 is 7 × 4, doubling twice.
- If you answered 3.5
- 3.5 halves 7; the second equation is the first DOUBLED.
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