Question

Solve the following system of equations.
2x – 3y + z = –1
3x + 2y + 2z = –1
x – y – 3z = –4

Answer 1

2x - 3y + z = -1 -->(-2)
3x + 2y + 2z = -1
--------------------
-4x + 6y - 2z = 2 (result of multiplying by -2)
3x + 2y + 2z = -1
--------------------add
-x + 8y = 1

3x + 2y + 2z = -1 -->(3)
x - y - 3z = -4 -->(2)
--------------------
9x + 6y + 6z = -3 (result of multiplying by 3)
2x - 2y - 6z = -8 (result of multiplying by 2)
--------------------add
11x + 4y = -11

-x + 8y = 1
11x + 4y = -11 -->(-2)
---------------------
-x + 8y = 1
-22x - 8y = 22 (result of multiplying by -2)
-------------------
-23x = 23
x = -1

-x + 8y = 1
-(-1) + 8y = 1
1 + 8y = 1
8y = 1-1
8y = 0
y = 0/8
y = 0

2x - 3y + z = -1
2(-1) - 3(0) + z = -1
-2 - 0 + z = -1
-2 + z = -1
z = -1 + 2
z = 1

check.....
3x + 2y + 2z = -1
3(-1) + 2(0) + 2(1) = -1
-3 + 0 + 2 = -1
-3 + 2 = -1
-1 = -1 (correct)

x = -1, y = 0, z = 1 or (-1,0,1)

Answer 2

any questions ?

Answer 3

holy crap you are really good at this thank you so much!

Answer 4

you are very welcome...glad I could help :)