Question

Please I am desperate! Check my answer.
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

Answer 1

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.

Answer 2

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).

Answer 3

If we solve answer B for y:

21x + 3 = 2y
(21/2)x + (3/2) = y which is not the same as the original.

Answer 4

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!

Answer 5

Wow, thank you, that makes so much more sense.

Answer 6

no problem, good luck!