Question

Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions involving one parameter, enter the solution using t for the last variable. If the solution involves two parameters, add s for the second to last variable.)

4x−8y−24z=−20
x−2y−6z=−5
3x−6y−18z=15

Answer 1

By inspection, we see that the first equation is a linear combination (4 times) the second equation. Similarly, the third equation can be obtained by multiplying equation 2 three times.

Therefore the equations represent 3 coincident lines:
x-2y-6z=-5
Let z = t, and y = s, then we can solve for x in terms of s and t:
x = -5 +2s + 6t
y = s
z = t

Answer 2

Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)
x + 2y + z = −2
−2x − 3y − z = 2
4x + 8y + 4z = −8
(x, y, z) =