Question

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

Answer 1

Answer:

• 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