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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 5/5

The system ax+by=1ax + by = 1 and bx+ay=1bx + ay = 1 has the same solution as x+y=1x + y = 1 and x=yx = y. What must be true?

  • A

    a=ba = b

  • B

    ab=1ab = 1

  • C

    a+b=2a + b = 2

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  • D

    a+b=1a + b = 1

Explanation

If x=y=12x = y = \frac{1}{2}, then a2+b2=1\frac{a}{2} + \frac{b}{2} = 1 → a+b=2a + b = 2.

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