Question

2x + 3y = 23
5x - 20 = 8y.
PLS SOLVE THIS SIMULTANEOUS LINEAR EQUATION IN SUBSTITUTION METHOD...​

Answer 1

Solution :

The two given equations are

    2x + 3y = 23 .....(i)

    5x - 20 = 8y .....(ii)

We have to find the values of x and y using Substitution method.

From equation no. (i), we get

    2x = 23 - 3y .....(iii)

From equation no. (ii), we get

    5x - 20 = 8y

⇒ 2 (5x - 20) = 2 × 8y

⇒ 10x - 40 = 16y

⇒ 5 (2x) - 40 = 16y

⇒ 5 (23 - 3y) - 40 = 16y, substituting the value of x from (iii) no. equation

⇒ 115 - 15y - 40 = 16y

⇒ 31y = 75

⇒ y = 75/31

From equation no. (iii), we get

    2x = 23 - 3 (75/31)

⇒ 2x   = 23 - (225/31)

⇒ 2x   = (23 × 31 - 225)/31

⇒ 2x   = (713 - 225)/31

⇒ 2x   = 488/31

⇒     x = 244/31

∴ the required solution is

     x = 244/31 , y = 75/31

Verification :

Putting x = 244/31, y = 75/31 in equation no. (i), we get

2 (244/31) + 3 (75/31)

= 488/31 + 225/31

= (488 + 225)/31

= 713/31

= 23

Similarly putting x = 244/31, y = 75/31 in equation no. (ii), we get

5 (244/31) - 20

= 1220/31 - 20

= (1220 - 20 × 31)/31

= (1220 - 620)/31

= 600/31

= 8 (75/31)

Hence, verified.

Answer 2

2x + 3y = 23

5x - 20 = 8y

___________________[GIVEN]

We have to find the value of x and y using Substitution method (means my putting values).

=> 2x + 3y = 23

=> 2x = 23 - 3y

=> x = $\dfrac{23\:-\:3y}{2}$ __(1)

=> 5x - 20 = 8y __(2)

Put value of equation (1) in equation (2) :

=> 5 $(\dfrac{23\:-\:3y}{2})$ - 20 = 8y

=> $\dfrac{115\:-\:15y}{2}$ - $\dfrac{20}{1}$ = 8y

=> $\dfrac{115\:-\:15y\:-40}{2}$ = 8y

=> 115 - 15y - 40 = 2(8y)

=> 75 - 15y = 16y

=> 75 = 16y + 15y

=> 75 = 31y

=> 31y = 75

y = $\dfrac{75}{31}$ __(3)

Put value of equation (3) in equation (2) :

=> 5x - 20 = (8) $(\dfrac{75}{31})$

=> 5x - 20 = $\dfrac{600}{31}$

=> 5x = $\dfrac{600}{31}$ + 20

=> 5x = $\dfrac{600\:+\:620}{31}$

=> 5x = $\dfrac{1220}{31}$

=> x = $\dfrac{1220}{31\:\times\:5}$

x = $\dfrac{244}{31}$

_________________________________

x = $\dfrac{244}{31}$

y = $\dfrac{75}{31}$

_____________________[ANSWER]