Question bank / Linear equations in two variables

Math · AlgebraEasy

The point (k,2k)(k, 2k) lies on the graph of 3x+2y=213x + 2y = 21 in the xyxy-plane. What is the value of kk?

A

33

B

215\frac{21}{5}

C

77

D

2121

Show answer and explanation

Answer: A

Substitute x=kx = k and y=2ky = 2k: 3k+2(2k)=213k + 2(2k) = 21, so 7k=217k = 21 and k=3k = 3. Check: 3(3)+2(6)=213(3) + 2(6) = 21.

Choice B substitutes kk for yy instead of 2k2k, which gives 5k=215k = 21.

Why the other choices are wrong

  • B. This substitutes k for y instead of 2k, which gives 3k + 2k = 21.
  • C. 7 is the coefficient in 7k = 21. Divide 21 by 7 to find k.
  • D. 21 is the constant in the equation, not the value of k.
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