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jek_recluse [69]
3 years ago
14

Solve the system of equations algebraically. Show all of your steps

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
4 0
I am going to explain this using the substitution method, considering it appears to be the best in this situation.

We know (from the bottom equation) that y can equal 3x+20. Using this knowledge, we substitute the y in the top equation for 3x+20. Now, we have an equation that looks like this:

3x+20=x^2+2x

Now we need to move x to one side and then do some radicals (square roots).
Subtract the 2x on the right (since it is smaller, negatives = NONONO), which will give you

x+20=x^2

Now, we take the square root of both sides to get

rad(x+20)=x

Now we have to simplify. 20 doesn't have a square root, but 4 goes into 20, and 4 has a square root of 2. This now becomes

2rad(x+5)

This doesn't simplify any further... we have a problem... no way to isolate x as far as my knowledge goes... Sorry, can't help you any further than that, but another person or your teacher might be able to. R.I.P...
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3 turtles walking.
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a plane flying with the wind travels 630 mi in 1.5hrs. Flying against the wind , the plane travels 1120 mi in 4hrs. Find the rat
Flauer [41]
\bf \begin{cases}
r=\textit{rate of the plane}\\
w=\textit{rate of the wind}\\
\end{cases}
\\\\

\begin{array}{ccccllll}
&distance&rate&time(hrs)\\
&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\
\textit{with wind}&630&r+w&1\frac{1}{2}\\
\textit{against wind}&1120&r-w&4
\end{array}


\bf thus  \begin{cases}
630=(r+w)1\frac{1}{2}\to 630=(r+w)\frac{3}{2}
\\\\
1120=(r-w)4\\
--------------\\
630=(r+w)\frac{3}{2}\implies 630\cdot \frac{2}{3}=r+w\\
420=r+w\implies \boxed{420-w}=r\\
--------------\\
thus\\
--------------\\
1120=(r-w)4\implies 1120=4r-4w
\\\\
1120=4(\boxed{420-w})-4w
\end{cases}


solve for "w", to find the wind's speed rate,

so hmmm what's the plane's rate?  well 420 - w = r  :)
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