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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 5/5

The system kx+3y=9kx + 3y = 9 and 4x+2y=64x + 2y = 6 has a unique solution where x=0x = 0. What is kk?

  • A

    3

  • B

    1

  • C

    Any value of kk

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  • D

    0

Explanation

From eq2: 4(0)+2y=64(0) + 2y = 6 → y=3y = 3. From eq1: k(0)+9=9k(0) + 9 = 9, true for any kk. So any kk (provided unique-solution: k≠6k \neq 6 from coefficient ratios).

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