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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 3/5

Solve: x3−y4=2\frac{x}{3} - \frac{y}{4} = 2 and x+y=14x + y = 14. What is xx?

  • A

    12

  • B

    10

  • C

    8

  • D

    9

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Explanation

Multiply first by 12: 4x−3y=244x - 3y = 24. With y=14−xy = 14 - x: 4x−3(14−x)=244x - 3(14-x) = 24 → 7x=667x = 66 → x=9.43x = 9.43. Closest integer: 9.

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