Question

Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11

i have 0 clue how to do this at all.

Answer 1

would use the elimination method. Eliminating z

equation (1) x 4 - equation (2)

8x + 4y + 4z = -28
- x - 3y + 4z = -14
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7x + 7y = -14 (4)

and then equation (1) x 3 + equation (3)

6x + 3x + 3z = -21
x - 2y - 3z = -11
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7x + y = -32 (5)

now you have 2 equations in 2 unknowns

7x + 7y = -14 (4)
7x + y = -32 (5)

then equation (4) - equation (5) to eliminate x

6y = 18

y = 3

substitute into equation (5)

7x + 3 = -32

7x = -35

x = -5

substitute into equation 1 to find z

2(-5) + 3 + z = - 7

- 7 + z = -7

z = 0

then the solution is

x = -5, y = 3 and z = 0