Question

4x-3y=23 and x+2y=3 by using subtitution method??​

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equations are

$\rm :\longmapsto\:4x - 3y = 23 - - - (1)$

and

$\rm :\longmapsto\:x + 2y = 3$

$\bf\implies \:x = 3 - 2y - - - (2)$

On substituting (2) in (1), we get

$\rm :\longmapsto\:4(3 - 2y) - 3y = 23$

$\rm :\longmapsto\:12 - 8y - 3y = 23$

$\rm :\longmapsto\:12 - 11y = 23$

$\rm :\longmapsto\:- 11y = 23 - 12$

$\rm :\longmapsto\:- 11y = 11$

$\bf\implies \:y \: = \: - \: 1$

On substituting the value of y in equation (2), we get

$\rm :\longmapsto\:x = 3 - 2( - 1)$

$\rm :\longmapsto\:x = 3 + 2$

$\bf\implies \:x \: = \: 5$

Hence,

$\begin{gathered}\begin{gathered}\bf\: Solution \: is \: -\begin{cases} &\sf{x \: = \: 5} \\ \\ &\sf{y \: = \: - \: 1} \end{cases}\end{gathered}\end{gathered}$

Verification :-

Consider equation (1), we have

$\rm :\longmapsto\:4x - 3y = 23$

On substituting the values of x and y, we get

$\rm :\longmapsto\:4(5)- 3( - 1)= 23$

$\rm :\longmapsto\:20 + 3= 23$

$\bf\implies \:23 = 23$

Hence, Verified

Now, Consider equation (2), we have

$\rm :\longmapsto\:x + 2y = 3$

On substituting the values of x and y, we get

$\rm :\longmapsto\:5 + 2( - 1)= 3$

$\rm :\longmapsto\:5 - 2= 3$

$\bf\implies \:3 = 3$

Hence, Verified

Answer 2

Answer:

$\large\underline{\sf{Solution-}}$

Given pair of linear equations are

$\rm :\longmapsto\:4x - 3y = 23 - - - (1)$

and

$\rm :\longmapsto\:x + 2y = 3$

$\bf\implies \:x = 3 - 2y - - - (2)$

On substituting (2) in (1), we get

$\rm :\longmapsto\:4(3 - 2y) - 3y = 23$

$\rm :\longmapsto\:12 - 8y - 3y = 23$

$\rm :\longmapsto\:12 - 11y = 23$

$\rm :\longmapsto\:- 11y = 23 - 12$

$\rm :\longmapsto\:- 11y = 11$

$\bf\implies \:y \: = \: - \: 1$

On substituting the value of y in equation (2), we get

$\rm :\longmapsto\:x = 3 - 2( - 1)$

$\rm :\longmapsto\:x = 3 + 2$

$\bf\implies \:x \: = \: 5$

Hence,

$\begin{gathered}\begin{gathered}\bf\: Solution \: is \: -\begin{cases} &\sf{x \: = \: 5} \\ \\ &\sf{y \: = \: - \: 1} \end{cases}\end{gathered}\end{gathered}$

Verification :-

Consider equation (1), we have

$\rm :\longmapsto\:4x - 3y = 23$

On substituting the values of x and y, we get

$\rm :\longmapsto\:4(5)- 3( - 1)= 23$

$\rm :\longmapsto\:20 + 3= 23$

$\bf\implies \:23 = 23$

Hence, Verified

Now, Consider equation (2), we have

$\rm :\longmapsto\:x + 2y = 3$

On substituting the values of x and y, we get

$\rm :\longmapsto\:5 + 2( - 1)= 3$

$\rm :\longmapsto\:5 - 2= 3$

$\bf\implies \:3 = 3$

Hence, Verified