SAT Mathematics Practice Test 3

Subtracting the sides of $3\mathit{y}+\mathit{c}=5\mathit{y}-7$
from the corresponding sides of $3\mathit{x}+\mathit{b}=5\mathit{x}-7$ gives $\left(3\mathit{x}-3\mathit{y}\right)+\left(\mathit{b}-\mathit{c}\right)=\left(5\mathit{x}-5\mathit{y}\right)$.
Since $\mathit{b}=\mathit{c}-\frac{1}{2},$ or $\mathit{b}-\mathit{c}=-\frac{1}{2}$ it follows that $\left(3\mathit{x}-3\mathit{y}\right)+\frac{1}{2}=\left(5\mathit{x}-5\mathit{y}\right)$.
Solving this equation for x in terms of y gives $\mathit{x}=\mathit{y}-\frac{1}{4}$,
Therefore ,$\mathit{x}$ is $\mathit{y}$ minus $\frac{1}{4}$
Choices B, C, and D are incorrect and may be the result of making a computational error when solving the equations for x in terms of y