Question

X-y+z=5
-2x-y-z=-6
3x+3y-2z=-5

Solve algebraically.

Answer 1

ohhhh...these are a pain in the butt. Very time consuming.

here we go...

x - y + z = 5 ----- multiply by -1
-2x - y - z = -6
--------------
-x + y - z = -5 (result of multiplying by -1)
-2x - y - z = -6
--------------add
-3x - 2z = - 11

x - y + z = 5 ---- multiply by 3
3x + 3y - 2z = -5
----------------
3x - 3y + 3z = 15 (result of multiplying by 3)
3x + 3y - 2z = -5
---------------add
6x + z = 10

-3x - 2z = -11
6x + z = 10 ---- multiply by 2
---------------
-3x - 2z = -11
12x + 2z = 20 (result of multiplying by 2)
--------------add
9x = 9
x = 1

6x + z = 10
6(1) + z = 10
6 + z = 10
z = 10 - 6
z = 4

x - y + z = 5
1 - y + 4 = 5
5 - y = 5
-y = 0
y = 0

check...
-2x - y - z = -6
-2(1) - 0 - 4 = -6
-2 - 4 = -6
-6 = -6 (correct)

so x = 1, y = 0, and z = 4

Answer 2

It would probably be easier to use matrices....I am just not too good with those

Answer 3

I was extremely confused, thank you so much for clearing it up for me. This is a huge help. Thank you so much! I'm not too great at matrices, either.