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Linear Equations in One Variable

SAT Math· difficulty 5/5

For what values of aa and bb does a(x−3)+4=5x+ba(x - 3) + 4 = 5x + b have infinitely many solutions?

  • A

    a=5a = 5, b=11b = 11

  • B

    a=5a = 5, b=−4b = -4

  • C

    a=5a = 5, b=−11b = -11

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  • D

    a=−5a = -5, b=11b = 11

Explanation

Expand: ax−3a+4=5x+bax - 3a + 4 = 5x + b. For all xx: a=5a = 5 and −3a+4=b-3a + 4 = b, so b=−15+4=−11b = -15 + 4 = -11.

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