SOLUTION: Not sure if i did this right mind helping me out? Solve the system of equations {x+y+z=-3 {x-y+3z=-13 {4x+4y+4z=-15 My answer looks like this x=-2,y=3,z=-4

Question 622962: Not sure if i did this right mind helping me out?
Solve the system of equations
{x+y+z=-3
{x-y+3z=-13
{4x+4y+4z=-15
My answer looks like this
x=-2,y=3,z=-4
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
.
Here is how to check your answer. If you got it right, the values you found for x, y, and z will make every equation in the system true.
.
Just substitute -2 for x, 3 for y, and -4 for z in each equation.
x+y+z=-3
(-2)+(3)+(-4)=-3
-3=-3
Check!!
.
x-y+3z=-13
(-2)-(3)+3(-4)=-13
-2-3-12=-13
-17=-13
Oops...Your solution doesn't work in this equation.
.
x=-2,y=3,z=-4
.
We can see that there is a problem with your calculations because the solution must work in every equation.
.
Let's start with the elimination method. Multiply every term in equation {A} by -4.
{A} x+y+z=-3 ---------------> -4x-4y-4z=12
{B} x-y+3z=-13
{C} 4x+4y+4z=-15 -----------> 4x+4y+4z=-15
.
Add equations {A} and {C}
-4x-4y-4z=12
4x+4y+4z=-15
.
Since the variables all cancel out (-4x+4x=0, etc.) we have
0=-3
.
This result tells us that these two equations have no points in common. In 2-D, this is analogous to parallel lines. Your system has no single point (x,y,z) solution.
.
Here are some pictures of what solutions to systems of equations with three variables can look like:
http://www.mathwarehouse.com/algebra/planes/systems/three-variable-equations.php
.
Hope this helps! Feel free to email me if you have questions about this explanation.
.
Ms.Figgy
math.in.the.vortex@gmail.com

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