Question

how do I Solve Systems of Equations by Elimination?!

Answer 1

Can someone solve these equations by elimination word by word?! x+y=2 & 2x+3y=12

Answer 2

\(\large
\begin{array}{llll}
x&+y&=&2\\
2x&+3y&=&12\\
\hline\\
\square?&\square?&&\square?
\end{array}\)

notice that, the top and bottom equations are adding each other there
to get some result at the bottom

now, what we want, is to get a 0 on say the "x column"
so that, something added to the say "2x", will yield us 0, that is \(\large \begin{array}{llll}\square? \\ 2x\\ \hline\\ 0\end{array}\)

Answer 3

what "something" do you think we need to make that SUM to 0?
that is
"something" + 2x = 0

what should that "something" be?

Answer 4

your equation x+y=2 and 2x+3y=12
now our aim is to make one term on equation equal to other so that we can cancel it , for that we will multiply first equation by 2\[2(x+y=2)\]\[2x+2y=4\] consider it as eq 3, now subtract eq 2 from 3 or vice versa \[(2x+2y=4)-(2x+3y=12)\]\[2x+2y-2x-3y=4-12\]\[-y=-4\]\[y=4\] now for x we will substitute ot in eq 1 or any eq you want \[x+4=2\]\[x=2-4\]\[x=-2, y=4\]