If 2x+y=23 and 4x-y=19, what are the values of 5y-2x and yx-2 ?

Given system of equations are,

2 x + y = 23

...

(1)

4 x - y = 19

...

(2)

Now, adding both the equation will have, +y and -y will cancel out each other. We have,

6 x = 42

x = 7

Now, substituting

x = 7

in in equation

(1) .

\Rightarrow 2 (7) + y = 23

\Rightarrow 14 + y = 23

\Rightarrow y = 9

Now, substituting

x = 7

and

y = 9

5 y - 2 x

\Rightarrow 5 (9) - 2 (7)

\Rightarrow 45 - 14

\Rightarrow 31

Now substituting

x = 7

and

y = 9

\frac{y}{x} - 2,

\Rightarrow \frac{9}{7} - 2

\Rightarrow \frac{9 - 14}{7}

\Rightarrow \frac{- 5}{7}

Therefore,

5 y - 2 x = 31

and

\frac{y}{x} - 2 = \frac{- 5}{7}

.
The correct option is 2.

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