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Question: Which equation would make this system consistent and dependent? Equation: 2/3y = 7x - (1/2).
Choices: A. 42x - 4y = 3
B. 21x = 2y - 3
D. y = (21/2)x - (3/2)
My Answer: D
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A system is consistent and dependent if the two equations are identical. So we must find an answer choice that is the same as the original equation.
As it is written, our original equation is very messy, using some algebra, we can write:
(2/3)y = 7x - (1/2) as
2y = 21x - (3/2)
y = (21/2)x - (3/4)
Answer choice D is close, but not quite right (it has 3/2 instead of 3/4).
If we solve answer B for y:
21x + 3 = 2y
(21/2)x + (3/2) = y which is not the same as the original.
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That leaves us with only one answer left:
A. 42x - 4y = 3
42x = 3 + 4y
42x - 3 = 4y
(42/4)x - (3/4) = y
reversing the equation to make the y look right (we can do this since it is equal)
y = (42/4)x - (3/4)
y = (21/2)x - (3/4)
Which is the same as our original equation and we are done!