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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 5/5

The system xa+yb=1\frac{x}{a} + \frac{y}{b} = 1 and xb+ya=1\frac{x}{b} + \frac{y}{a} = 1 (with a≠ba \neq b) has solution:

  • A

    x=y=aba+bx = y = \frac{ab}{a+b}

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  • B

    x=y=1x = y = 1

  • C

    x=a+bx = a + b, y=a−by = a - b

  • D

    x=a,y=bx = a, y = b

Explanation

By symmetry x=yx = y. Sub into first: x(1a+1b)=1x(\frac{1}{a} + \frac{1}{b}) = 1 → x⋅a+bab=1x \cdot \frac{a+b}{ab} = 1 → x=aba+bx = \frac{ab}{a+b}.

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