Question

Solve the system of linear equations:
4x-y+z=-5
2x+2y+3z=10
5x-2y+6z=1

Answer 1

Add second two equations; get an equation with x and z. Let x or z become 0, now you have just one variable.

Answer 2

Do you know any linear algebra? Namely, gaussian elimination?

Answer 3

I remember learning about it, I don't really know how to do it though.

Answer 4

Hmmmm...I am not sure how to do matrices in this but I can give you an idea of how to do it and can link you to some examples. What the idea is: You "augment" your equations and solutions into a matrix. By that I simply mean, you make a matrix with coefficient rows. For example, take your first equation. The first row of this matrix would be 4 -1 1 -5.

Answer 5

I know matrices, it's so much easier than having to solve it algebraically or whatever :P

Answer 6

x = -1, y = 3 and z = 2 is the answer

Answer 7

:) So you can take the coefficients from all your equations and make a matrix. Then reduce it to whats called "row echelon" form. All this shows is that all of your entries in the lower left OR upper right are all zeros. What this tells you, is one variable as a number so either x or z. From there you can back substitute. Let me see if I can find you some examples.

Answer 8

Ohhhh i got it! I forgot about row echelon :D thanks :)

Answer 9

You're welcome :) Just let me know if you want those links.

Answer 10

matrices are a pain to type out; but if you can figure the equation editors version of it it might work :)

\[\left|
\begin{array}c
a & b & c & d \\
e & f & g & h \\
i & j & k & l \\
m & n & o & p
\end{array}
\right|\]


\[\left|
\begin{array}c
a & b & c & d \\
e & f & g & h \\
i & j & k & l \\
m & n & o & p
\end{array}
\right|\_]
^remove this(_) and if formats like above: