The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system.

1 0 0 5 18

0 1 0 4 - 5

0 0 1 0 - 9

0 0 0 0 0

Enter the solution of the system below.

Use w for the parameter

x=

y=

z=

W is any real number

x = 18 - 5w y = - 5 - 4w z = - 9

Step-by-step explanation:

Since w is the parameter, we assume the equations are written in the form ...

ax + by + cz + dw = e

This means the reduced matrix is telling you ...

x + 5w = 18

y + 4w = - 5

z = - 9

The first two of these equations can be solved for x and y by subtracting the w term:

x = 18 - 5w

y = - 5 - 4w