Question

What is the solution of the system of equation?
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1

Answer 1

using linear algebra, put it in rref to get your answer

the other method would be to try to cancel one of the variables out
so if you multiply the first equation be -1, and then add all 3 of them you will get an equation of one varable, then substitute it in to the other equations and try to cancel out another variable

Answer 2

Can you help me step-by-step?

Answer 3

yea sure

first multiply the first equation by -1 and then add all 3 equations together

Answer 4

can you do it for me?

need to make sure you understand what im trying to say

Answer 5

So 3(-1)+2(-1)+(-1)=7

Answer 6

when you multiply the equation by -1, you need to multiply both sides of the equation
\[-1(3x+2y+z) = 7(-1)\]
simplifies to
\[-3x - 2y\]

Answer 7

sorry this is the simiplied form the rest got cutoff for some reason
\[-3x - 2y -z = -7 \]

Answer 8

oh, okay, that makes sense

Answer 9

now that you multiply both sides of the first equation by -1
you want to add all 3 equations together

Answer 10

lol this might be a bit of work to do unless i show you how to do it through linear algebra

just solve for y in this new equation
\[y = \frac{ -3 }{ 5 } - \frac{ 5 }{ 3 }x \]
plug it in the first equation

Answer 11

I'm not sure how to solve that...

Answer 12

yea.. sorry i dont think i can do it the usual way without linear algebra.. i can show you using matrices if you like?