SOLUTION: Please help me solve this equation: Solve the following system of equations using the back substitution method. {{{ x+2y-3z=9 }}} {{{ 2x-y+z=0 }}} {{{ 4x-y+z=4 }}} Thanks

Algebra ->  Matrices-and-determiminant -> SOLUTION: Please help me solve this equation: Solve the following system of equations using the back substitution method. {{{ x+2y-3z=9 }}} {{{ 2x-y+z=0 }}} {{{ 4x-y+z=4 }}} Thanks       Log On


   

Question 352072: Please help me solve this equation:
Solve the following system of equations using the back substitution method.
+x%2B2y-3z=9+
+2x-y%2Bz=0+
+4x-y%2Bz=4+
Thanks so much!!
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2B2y-3z=9+
+2x-y%2Bz=0+
+4x-y%2Bz=4+

we substitute backwards, from 2 variables : equ (3) leads to -y+z=4-4x

putting -y+x in equ (2) : 2x+4-4x=0 => -2x=-4 => x=2.

Substituting x in the whole system, we get a consistent system in y,z :

2y+3z=7
-y+z=-4
(-y+z=-4)

then we can use standard methods :
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++2%5Cy+%2B+3%5Cz+=+7%2C%0D%0A++++-1%5Cy+%2B+1%5Cz+=+-4+%29%0D%0A++We'll use substitution. After moving 3*z to the right, we get:
2%2Ay+=+7+-+3%2Az, or y+=+7%2F2+-+3%2Az%2F2. Substitute that
into another equation:
-1%2A%287%2F2+-+3%2Az%2F2%29+%2B+1%5Cz+=+-4 and simplify: So, we know that z=-0.2. Since y+=+7%2F2+-+3%2Az%2F2, y=3.8.

Answer: system%28+y=3.8%2C+z=-0.2+%29.