Question

$y=3x-1$
$\frac{1}{2}y+x=1$
Solving the above equations simultaneously yields a solution given by $(x,y)$, then determine the value of $y-x$.

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{1}{5}$
• D. $\frac{5}{4}$

Answer 1

Answer: (C)

$\frac{1}{5}$

$y=3x-1$

$\Rightarrow y-3x=-1$..............................................(1)

$\frac{1}{2}y+x=1$

$\Rightarrow y+2x=2$...............................................(2)

$y=3x-1\Rightarrow y-3x=-1$

$\frac{1}{2}y+x=1\Rightarrow y+2x=2$

Substract equation (1) and (2) we get

5x=3

Or $x=\frac{3}{5}$

Put $x=\frac{3}{5}$ in equation (1) we get

$y=3\times \frac{3}{5}-1\Rightarrow y=\frac{4}{5}$

Then $y-x=\frac{4}{5}-\frac{3}{5}=\frac{1}{5}$