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

Answer 1

...

Answer 2

@SmoothMath

Answer 3

I got you

Answer 4

K thx. :)

Answer 5

Take one of the equations and solve for one variable in terms of the other 2. For example:
2x + y + z = –7
y=-2x-z-7
Now plug that in for y in either of the next equations and solve for another variable:
x – 3y + 4z = –14 becomes
x-3(-2x-z-7)+4z=-14
x+6x+3z+21+4z=-14
7x+7z=7
x=1-z

Now go to x – 2y – 3z = –11
and use the values we got for x and y

(1-z)-2(-2x-z-7)-3z=-11 and solve for z.
1-z+4x+2z+14-3z=-11
1-2z+4(1-z)+14
1-2z+4-4z+14=-11
19-6z=-11
19=-11+6z
30=6z
z=5

And then you plug in the value you got for z to find x and y. This is the super long way to do it. If you know how to use matrices and row reduction it is much faster.

Answer 6

Do you get it?