Question

PLEASE HELP!
Use elimination to solve the system of equations

-3x+ y + 7z = -20
5x - 2y - z = 34
-x + y +4z = -8

Answer 1

have you done elimination on a system of equations with 2 variables?

Answer 2

yes

Answer 3

so the way you'd 3 variables is by picking 2 first, eliminate one
pick another 2, eliminate the same one
then solve the 2 resulting two-variable functions

-3x+ y + 7z = -20 <--- let's use this one
5x - 2y - z = 34 <--- and this one
-x + y +4z = -8

\(\bf \begin{array}{llll}
-3x+ y + 7z = -20&&-3x+ y + 7z = -20\\
\quad 5x - 2y - z = 34&\times 7\implies &35x-14y-7z=238\\
\hline\\
&&32x-13y+0z=218\\ \quad \\
\color{blue}{32x-13y=218}
\end{array}\)

Answer 4

so for our next pair of functions, let us use

-3x+ y + 7z = -20
5x - 2y - z = 34 <--- this one
-x + y +4z = -8 <--- and this one

so \( \begin{array}{llll}
\quad 5x - 2y - z = 34&\times 4\implies &20x-8y-4z=136\\
-x + y +4z = -8&&-x + y +4z = -8\\
\hline\\
&&19x-7y+0z=128\\ \quad \\
\color{blue}{19x-7y=128}
\end{array}\)

Answer 5

so once you have those 2 RESULTANT functions, you can solve the system of 2 variables by elimination or substitution to get both variables

once you have "x" and "y", you can plug those in on any of the 3 original functions to get "z"

Answer 6

Thank you!

Answer 7

yw