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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 4/5

For what value of aa do the lines ax+2y=6ax + 2y = 6 and 3x−4y=123x - 4y = 12 NOT intersect (parallel)?

  • A

    a=32a = \frac{3}{2}

  • B

    a=23a = \frac{2}{3}

  • C

    a=−32a = -\frac{3}{2}

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  • D

    a=−23a = -\frac{2}{3}

Explanation

Slope of eq1 =−a/2= -a/2, slope of eq2 =3/4= 3/4. Equal: −a/2=3/4-a/2 = 3/4 → a=−3/2a = -3/2.

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