Question

Question 7
If 2x + y = 23 and 4x – y = 19, then find the values of 5y – 2x and $\frac{y}{x}$- 2.

Answer 1

Given equations are
2x + y = 23 and
4x – y = 19
On adding both equations, we get
$6x=42$
$\Rightarrow$ x = 7
Put the value of x in the first equation, we get
$2\left(7\right)+y=23\Rightarrow 14+y=23\Rightarrow y=23–14\Rightarrow y=9$

Substituting $x=7$ and $y=9$ in the equations whose values have to be found, we get,

$5y–2x=(5\times 9)–(2\times 7)=45–14=31$

$\frac{y}{x}-2=\frac{9}{7}-2=\frac{9-14}{7}=-\frac{5}{7}$

Hence, the values of $5y-2x$ and $(\frac{y}{x}-2)$ are 31 and $\frac{-5}{7}$ respectively.