Linear Equations in One Variable

SAT Math· difficulty 5/5

The system {2x+3y=124x+ky=20\begin{cases} 2x + 3y = 12 \\ 4x + ky = 20 \end{cases} has no solution. What is the value of kk?

  • A

    3

  • B

    8

  • C

    6

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  • D

    5

Explanation

For no solution, lines are parallel but distinct. Multiply first by 2: 4x+6y=244x + 6y = 24. So k=6k = 6 and constants differ (242024 \ne 20).

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