Question

solve the system by elimination

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

I don't understand this at all if someone could come up with a full explanation ill greatly appreciate it.

Answer 1

do you know how to solve by elimination with 2 variables?

Answer 2

Im sorry i barely understand this

Answer 3

well... do you even know what solving by elimination mean?

Answer 4

yes i do

Answer 5

have you done any with only 2 variables?

Answer 6

yes i dont know how to do it with the three variables

Answer 7

the way it works is, off the 3 equations, you grab 2 at a time a time, and eliminate 1 variable

then you go and grab 2 more and eliminate same 1 variable

-2x+2y+3z=0 <---- let's use this one
-2x-y+z=-3 <---- and this one
2x+3y+3z=5


\(\begin{array}{llll}
-2x+2y+3z=0&\implies &-2x+2y+3z=0\\
-2x-y+z=-3& \times -3\implies &6x+3y-3z=9\\
\hline\\
&&4x+5y+0=9\\ \quad \\
\color{blue}{4x+5y=9}


\end{array}\)

Answer 8

now let's use grab another set of 2.... let's grab this time

-2x+2y+3z=0 <--- this one again
-2x-y+z=-3
2x+3y+3z=5 <--- and this one this time

\(\begin{array}{llll}
-2x+2y+3z=0&\implies &-2x+2y+3z=0\\
2x+3y+3z=5& \times -1\implies &-2x-3y-3z=-5\\
\hline\\
&&-4x-y+0=-5\\ \quad \\
\color{blue}{-4x-y=-5}


\end{array}\)

Answer 9

and now you just grab those 2 RESULTANT equations, with only 2 variables and solve for either, then get the other, and then plug both in to get "z" in any of the 3 equations above

Answer 10

thank you i sort of understand it now

Answer 11

i got x=1.5 y=-1 z=1.6 is that right?