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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 3/5

For what value of kk does the system 3x+ky=93x + ky = 9 and 6x+4y=76x + 4y = 7 have no solution?

  • A

    k=4k = 4

  • B

    k=3k = 3

  • C

    k=1k = 1

  • D

    k=2k = 2

    check_circle

Explanation

Parallel lines: 36=k4≠97\frac{3}{6} = \frac{k}{4} \neq \frac{9}{7}. From 12=k4\frac{1}{2} = \frac{k}{4}: k=2k = 2. Check: 9/7≠1/29/7 \neq 1/2. So k=2k = 2.

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