Question

please, please help....cannot figure this out...keep getting negative numbers.
Solve by the system of elimination
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answer 1

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

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

now let's try

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


\(\bf \begin{array}{llll}
-2x+2y+3z=0&\implies &-2x+2y+3z=0\\
2x+3y+3z=5&\times -1\implies &-2x-3y-3z=-5\\
\hline\\
&&0-y+0=9\\ \quad \\
\color{blue}{y =9}
\end{array}
\)

Answer 2

hmmm one sec... on the 2nd one

Answer 3

\( \begin{array}{llll}
-2x+2y+3z=0&\implies &-2x+2y+3z=0\\
2x+3y+3z=5&\times -1\implies &-2x-3y-3z=-5\\
\hline\\
&&-4x-y+0=9\\ \quad \\
\color{blue}{-4x-y =9}
\end{array}\)

Answer 4

so now we have a system of equations of 2 variables,

4x + 5y = 9
-4x-y = 9

let's us solve that by elimination, we can add them straight up

\(\bf \begin{array}{llll}
4x + 5y = 9\\
-4x-y = 9\\
\hline\\
0x+4y=18\implies y = \cfrac{18}{4}\implies \color{green}{{\bf y = \cfrac{9}{2}}}\\ \quad \\
\textit{let us use our found "y" in say... }\quad 4x + 5y = 9\\ \quad \\
4x+5\left(\cfrac{9}{2}\right)=9\implies 4x=9-\cfrac{45}{2}\implies 4x = -\cfrac{27}{2}\\ \quad \\
\color{green}{{\bf x = -\cfrac{27}{8}}}
\end{array}\)

Answer 5

so now that we have our "x" and "y", let use use it on either... say... hmm \(\bf -2x-y+z=-3\)

\(\bf \implies -2\left(-\cfrac{27}{8}\right)-\left(\cfrac{9}{2}\right)+z=-3\implies \cfrac{27}{4}-\cfrac{9}{2}+z=-3\\ \quad \\
z=-3-\cfrac{27}{4}+\cfrac{9}{2}\implies z = -\cfrac{12}{4}-\cfrac{27}{4}+\cfrac{18}{4}\implies \color{green}{z = -\cfrac{21}{4}}\)

Answer 6

so 2 ended up negative... and 1 is positve, if that's what you got, it was ok

Answer 7

Thank you so much.....I kept coming up with those negative numbers and thought I was doing something wrong. This helps to understand it better. Thanks again.

Answer 8

yw