please help! solve the following system:?

Question

i'm kind of confused with this problem for algebra II. so can you guys help me pleasssseeee!!


solve the following system:

x+2y-2z=3
x+3y-4z=6
4x+5y-2z=3

Answer 1

One can prove that a linear combination of the first 2 equations will result in the 3rd equation except that is beyond the scope of Algebra II.

{EDIT} Likewise, one can prove that the matrix has no inverse because it is not singular.

Answer 2

You have to use substitution so
x = 3 + 2z -2y
so in line 32 substitute and you get
3 + 2z - 2y + 3y -4z = 6
Simplify to
-2z = y = 3 so
y = 3 + 2z
so in line 3
4x + 5(3 + 2z) - 2z = 3
simplify
4x + 15 + 8z = 3
4x + 8z + 12 = 0
4(3 + 2z - 2y) + 8z + 12 = 0
12 + 8z - 8y + 8z + 12 = 0
24 + 16Z - 8y = 0
We know that y = 3 + 2z so
24 + 16z - 8(3 + 2z) = 0 so
24 + 16z - 24 - 16z = 0
So 0 = 0

Sorry