Finite Math
posted by Dee .
Solve the system of linear equations, using the GaussJordan 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

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:
x2y6z=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