Question

If 2x+y=23 and 4x-y=19 find the values of 5y-2x and y/x-2

Answer 1

Answer:

Step-by-step explanation:

2x+y=23.........(1)

4x-y=19..........(2)

(1)+(2)

2x+y=23

4x-y=19

(+y and -y will be cancelled)

6x=42

x=42/6

x=7

(substituting the value of x in first equation)

2(7)+y=23

14+y=23

y=23-14

y=9

(substituting the value of x and y)

5(9)-2(7)           y/x-2  

=45-14             =9/7-2/1

=31                (taking lcm of 7,2)

                       =18/14-14/7

                       =18-14/7

                       =4/7      

Answer 2

$\bigstar$QUESTION:

If 2x+y=23 and 4x-y=19 find the values of 5y-2x and y/x-2

$\diamond$Finding the required value:-

Given equations are

⠀⠀➟2x+y=23⠀⠀⠀.....(1)

and➟4x-y= 19⠀⠀⠀⠀.......(2)

On adding both equation, we get

⠀⠀⠀⠀⠀

$\sf \implies6x = 42$

$\implies \sf x = \dfrac{42}{6} = 7$

Now, putting the value of x in equation (1) ,we get

$\sf : \implies2(7) + y = 23$

$\sf : \implies14 + y = 23$

$\sf:\implies \: y = 23 - 14 = 9$

We have, 5y-2x =5×9-2×7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=45-14=31

⠀⠀⠀⠀⠀

$\sf \: and \: \: \: \dfrac{y}{x} - 2 = \dfrac{9}{7} - 2$

$: \implies \sf \dfrac{9 - 14}{7} = \dfrac{ - 5}{7}$

⠀⠀⠀⠀⠀

Hence, the value of :-

$\mapsto \boxed{ \red{ \sf 5y - 2x = 31}}$

$\mapsto\boxed{ \sf \green{ \frac{y}{x} - 2 = \dfrac{ - 5}{7} }}$

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