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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 4/5

For the system 5x+ky=205x + ky = 20 and kx+5y=20kx + 5y = 20, infinitely many solutions occur when:

  • A

    k=5k = 5 only

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  • B

    k=5k = 5 or k=−5k = -5

  • C

    k=−5k = -5 only

  • D

    k=0k = 0 only

Explanation

Need scalar match: 5k=k5=2020=1\frac{5}{k} = \frac{k}{5} = \frac{20}{20} = 1. So k=5k = 5.

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