Question

hey there i'm kinda new here but here it goes how can i solve systems of equations

Answer 1

there r many methods i personally like to use matrices and gaussian elimination

Answer 2

can yo do it without a grap

Answer 3

*graph*

Answer 4

GRAPHS ARE RATHER IMPRECISE ... im gonna break that pinky

Answer 5

many systems are not graphable to begin with

Answer 6

sure for example suppose u have the system\[3x+2y=5,\]\[3y+2x=10,\]then using matrices and performin gaussian elimination u get\[\begin{pmatrix}
3 & 2 & 5\\
2 & 3 & 10
\end{pmatrix}\to\begin{pmatrix}
1 & 0 & -1\\
0 & 1 & 4
\end{pmatrix}\]so \(x=-1\) and \(y=4\)

Answer 7

hmm what is Gaussian elimination and can i use it during an 8th grade test

Answer 8

oh u in 8th grade??? nvm this is american college lvl

Answer 9

oh ha ha

Answer 10

im 14 they teach us that here in russia

Answer 11

wow im 14 too

Answer 12

that is so cool though

Answer 13

well i have to go but thanks anyway

Answer 14

yea its a very powerful technique

theyre never gonna give you more than 2 equation but u can use it to solve bigger systems like this one\[2x+y-z=8\]\[-3x-y+2z=-11\]\[-2x+y+2z=-3\]\[\begin{pmatrix}
2 & 1 & -1 & 8\\
-3 & 1 & 2 & -11\\
-2 & 1 & 2 & -3
\end{pmatrix}\to\begin{pmatrix}
1 & 0 & 0 & 2\\
0 & 1 & 0 & 3\\
0 & 0 & 1 & -1
\end{pmatrix}\]so \(x=2\), \(y=3\) and \(z=-1\)