linear equation

Question

consider following set of equations

$x_1+x_2+x_3=6$

$2x_1+2x_2+3x_3=14$

$3x_1+x_2+2x_3=14$

Solution for this set exists when value of $x_2$ is

Comments

Given screenshot is the detialed solution

Answer 1

X₂ will be 1

X₃=2, X₁=3

x1+x2+x3=6  or,2x1+2x2+2x3=12.............(i)
 

2x1+2x2+3x3=14.....................(ii)

solving (i) and (ii) we get X3=2

Now, from (i) x1+x2+x3=6 or, x1+x2=4...........(iii)

and 3x1+x2+2x3=14 or 3x1+x2=10.........(iv)

solving (iii) and (iv) we get x1=3

then from equation (i) we get x2=1