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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 5/5

For what values of kk does the system kx+y=1kx + y = 1 and x+ky=1x + ky = 1 have a unique solution?

  • A

    All real kk

  • B

    k≠1k \neq 1

  • C

    k≠−1k \neq -1

  • D

    k≠±1k \neq \pm 1

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Explanation

Determinant: k2−1=0k^2 - 1 = 0 when k=±1k = \pm 1. Unique solution requires k≠±1k \neq \pm 1.

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