The pair $3x + y = 1$ and $(2k - 1)x + (k - 1)y = 2k + 1$ has no solution. What is the value of $k$ ?

2Correct answerYour answer

\frac{1}{2}

Correct answerYour answer1Correct answerYour answer

-2

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

No solution needs $\frac{3}{2k - 1} = \frac{1}{k - 1} \neq \frac{1}{2k + 1}$ .
From the first equality: $3(k - 1) = 2k - 1$ , so $3k - 3 = 2k - 1$ and $k = 2$ .
Check: at $k = 2$ the second equation is $3x + y = 5$ , parallel to $3x + y = 1$ and different from it.

Worth noting

$-2$ comes from also setting the $y$ ratio equal to the constant ratio, which is the wrong pair of ratios to compare. $\frac{1}{2}$ and 1 just make one coefficient zero.

Concept: Parameter for an inconsistent pair of linear equations
Typical timeTypical: 120 s
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The rule this testsPairs of linear equations

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Ten questions from Linear and Quadratic Equations, at your own pace.

The pair 3x+y=13x + y = 13x+y=1 and (2k−1)x+(k−1)y=2k+1(2k - 1)x + (k - 1)y = 2k + 1(2k−1)x+(k−1)y=2k+1 has no solution. What is the value of kkk?

Explanation

The pair $3x + y = 1$ and $(2k - 1)x + (k - 1)y = 2k + 1$ has no solution. What is the value of $k$ ?