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