Question

solve the linear equation with substitution method - 2x+3y=23 and 5x-20=8y​

Answer 1

1. -2x + 3y=23

2.5x - 8y =20

1 equ ×8,

-16x + 24y=184

2 equ ×3,

15x - 24y=60

named that equation as 3 & 4,

3 + 4,

we get answer -1x=244

therfore x=-244

sub.x=-244 in 1equ

we get y=155

Answer 2

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