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 – 3y + 4z = –9
2x + y + 3z = 6
x – 4y + 3z = –9

Answer 1

I would use the elimination method because there is 3 unknown variables.
That is just my preference. You could use substitution or matrices also.

x - 3y + 4z = -9 -->(-2)
2x + y + 3z = 6
--------------
-2x + 6y - 8z = 18 (result of multiplying by -2)
2x + y + 3z = 6
--------------add
7y - 5z = 24

2x + y + 3z = 6
x - 4y + 3z = -9 -->(-2)
-----------------
2x + y + 3z = 6
-2x + 8y - 6z = 18 (result of multiplying by -2)
-----------------add
9y - 3z = 24

7y - 5z = 24 -->(3)
9y - 3z = 24 -->(-5)
----------------
21y - 15z = 72 (result of multiplying by 3)
-45y + 15z = - 120 (result of multiplying by -5)
----------------add
- 24y = - 48
y = -48/-24
y = 2

7y - 5z = 24
7(2) - 5z = 24
14 - 5z = 24
-5z = 24 - 14
-5z = 10
z = -2

x - 3y + 4z = -9
x - 3(2) + 4(-2) = -9
x - 6 - 8 = -9
x - 14 = -9
x = -9 + 14
x = 5

check...
2x + y + 3z = 6
2(5) + 2 + 3(-2) = 6
10 + 2 - 6 = 6
12 - 6 = 6
6 = 6 (correct)

x = 5, y = 2, and z = -2