Question

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

Answer 1

Step $1$ : Find the value of $x$ and $y$.

$2x+y=23$……………………………………………….equation $1$

$4x-y=19$……………………………………………….equation $2$

Add equation $1$ and equation $2$.

$$\begin{gathered} 2x+y+4x-y=23+19 \\ \Rightarrow 6x=42 \\ \Rightarrow x=7 \end{gathered}$$

Putting value of $x$ in equation$1$.

$$\begin{gathered} 2\left(7\right)+y=23 \\ \Rightarrow y=23-14 \\ \Rightarrow y=9 \end{gathered}$$

Step $2$ : Find the value of $5y-2x$.

$$\begin{gathered} 5y-2x=5\left(9\right)-2\left(7\right) \\ \Rightarrow 5y-2x=45-14 \\ \Rightarrow 5y-2x=31 \end{gathered}$$

Step $3$ : Find the value of $\frac{y}{x}-2$.

$$\begin{gathered} \frac{y}{x}-2=\frac{9}{7}-2 \\ \Rightarrow \frac{y}{x}-2=\frac{9-14}{7} \\ \Rightarrow \frac{y}{x}-2=-\frac{5}{7} \end{gathered}$$

Hence, the value of $5y-2x$ is $31$ and value of $\frac{y}{x}-2$is $-\frac{5}{7}$.