Question

Solve
X+2y+z=7
X+3z=11
2x-3y=1

Answer 1

hope u get it...........

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The solution is x = 2, y = 1 and z = 3.}}}$

Step-by-step explanation:

The given equations are :

$x+2y+z=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+3z=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\2x-3y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

From equations (ii) and (iii), we have

$x+3z=11\\\\\Rightarrow z=\dfrac{11-x}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

and

$2x-3y=1\Rightarrow y=\dfrac{2x-1}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the values of y and z from equations (iv) and (v) in equation (i), we get

$x+2\times\dfrac{2x-1}{3}+\dfrac{11-x}{3}=7\\\\\\\Rightarrow \dfrac{3x+4x-2+11-x}{3}=7\\\\\Rightarrow 6x+9=21\\\\\Rightarrow 6x=12\\\\\Rightarrow x=2.$

From equations (iv) and (v), we get

$z=\dfrac{11-2}{3}=\dfrac{9}{3}=3$

and

$y=\dfrac{2\times2-1}{3}=1.$

Thus, the required solution is

x = 2, y = 1, z = 3.

#Learn more

Question : Solve : x+2y+z=7;x+3z=11;2x-3y=1 in elimination / substitution/ multiplication.

Link : https://brainly.in/question/1240969.