Algebra practice question

Answer: 4

A system has no solution when the lines are parallel but different. The second equation's x-coefficient, 6, is 2 times the first's, 3. For the same slope, the y-coefficient must also be 2 times: k = 2(2) = 4. Then the left side is 2(3x + 2y) = 6x + 4y, which would equal 2(7) = 14 — but it's set to 20, so the lines are parallel and never meet.

Common wrong answers

If you answered 2

With k = 2 the second equation is 6x + 2y = 20, which has a different slope from the first, so the lines cross once.

If you answered 6

6 is the x-coefficient already in the second equation. The unknown is the y-coefficient, which must be twice 2.

If you answered 14

14 is what the right side would be if the second equation were exactly twice the first — that gives infinitely many solutions, not none. The question asks for k, the y-coefficient.

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