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

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

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

⇒Solution set

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2

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