Question

Find the solution set for
X + 2y + 3 z + w=1
3x - y +z+ w= 3

Answer 1

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

`x=(7-5 m-3 n)/(7)`

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

`y=(-8 m-2 n)/(7)`

⇒Solution set

`=((7-5 m-3 n)/(7),(-8 m-2 n)/(7), m, n)`