Question

If $2x+y=23$ and $4x-y=19$, find the values of $5y-2x$ and $\frac{y}{x}-2$.

• A. $36,-\frac{1}{3}$
• B. $31,-\frac{5}{7}$
• C. $38,\frac{6}{7}$
• D. None of these

Answer 1

The correct option is B $31,-\frac{5}{7}$

Given System of Equations are:
$2x+y=23$ ...$\left(1\right)$
$4x-y=19$ ...$\left(2\right)$
Now adding both the equation will have:
$6x=42$
$x=7$
Now substituting $x=7$ in in equation $\left(1\right)$
$\Rightarrow 2\left(7\right)+y=23$
$\Rightarrow 14+y=23$
$\Rightarrow y=9$
Now substituting $x=7$ and $y=9$ in $5y-2x$
$\Rightarrow 5\left(9\right)-2\left(7\right)$
$\Rightarrow 45-14$
$\Rightarrow 31$
Now Substituting Now substituting $x=7$ and $y=9$ in $\frac{y}{x}-2$
$\Rightarrow \frac{9}{7}-2$
$\Rightarrow \frac{9-14}{7}$
$\Rightarrow \frac{-5}{7}$