Answer with explanation:
The two equation whose solution set we have to find is:
x + 2y + 3 z + w=1
3x - y +z+ w= 3
as there are four variables and two equations.So,we will select any of two variables as independent variables and find the solution of other variables in terms of other.
Let, w=n
z=m
Then,
x+2 y=1 -3 m-n--------(1)
3 x-y =3-m-n----------------(2)
Multiplying equation (2) by 2
6 x -2 y=6-2 m-2n----------(2)
Adding (1) and (2)
7 x=7-5 m-3 n
[tex]x=\frac{7-5 m-3 n}{7}[/tex]
Multiplying equation (1) by 3
3 x+6 y=3 -9 m-3 n---------(1)
3 x-y =3-m-n----------------(2)
Equation (1)- Equation (2)
7 y= -8 m-2 n
[tex]y=\frac{-8 m-2 n}{7}[/tex]
⇒Solution set
[tex]=(\frac{7-5 m-3 n}{7},\frac{-8 m-2 n}{7}, m, n)[/tex]
