Question

Part 1: Explain, in complete sentences, which method you would use to solve the following system of equations. (1 point)

Part 2: Explain why you chose that method (1 point)

Part 3: Provide the solution to the system. (2 points)

x – 2y + z = 0
2x – 3y – 4z = –9
x + 2y – 5z = 0

Answer 1

If anyone can just explain to me how to solve it, i would really appreciate it.

Answer 2

Set up a 3 by 4 matrix.
The first row should be: 1 -2 1 0
Keep this row the same. We will use the 1 in the first space to eliminate the others in the first column.
Multiply row 1 by -2. The result is: -2 4 -2 0. Add this to row 2. Row 2 now becomes:
0 1 -6 -9. Keep this as row two.
Multiply row 1 by -1 and add this to row three. Row 3 now becomes: 0 4 -6 0.
Multiply row 2 by -4 and add the result to row 3. Row 3 now becomes: 0 0 18 36.
Divide row 3 by 18 and it becomes: 0 0 1 2.
This means that z=2.
Substitute into row 2: 0 1 -6 -9 and we get 1y -6z=-9
y-6*2=-9 or y-12=-9 or y=3.
Substitute in any of the equations(The easiest is row 1 so I'll use x-2y+z=0): x-2(3)+2=0 or x-6+2=0 or x-4=0 or x=4.
Final answer: (4, 3, 2)