What is the solution this system of equations? 2/3x+y=6

Ответ:

chrisayy

12.03.2022

$\bf \begin{cases}
\cfrac{2}{3}x+y=6\\[0.8em]
-\cfrac{2}{3}x-y=2
\end{cases}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\stackrel{\textit{using the first equation}}{\cfrac{2}{3}x+y=6}\implies y=6-\cfrac{2x}{3}
\\\\[-0.35em]
~\dotfill$

$\bf \stackrel{\textit{using the found \underline{y} in the second equation}}{-\cfrac{2x}{3}-\left( 6-\cfrac{2x}{3} \right)=2}\implies -\cfrac{2x}{3}-6+\cfrac{2x}{3}=2
\\\\\\
\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{-2x-18+2x=6}\implies -18\ne 6\impliedby \stackrel{\textit{system is inconsistent}}{\textit{no solutions}}$

if you set both equations to a y = mx+b, you'll notice the slope is the same, meaning the lines are parallel to each other, thus they never meet.

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Ответ:

kelyanthecrafte

03.05.2022

Mathematics

Step-by-step explanation:

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What is the solution this system of equations? 2/3x+y=6 and -2/3x-y=2

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