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2 years ago

How do you solve linear equations with substitutions?

Mathematics

1 answer:

Nostrana [21]2 years ago

5 0

Answer:

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

Step-by-step explanation:

Solve the following system by substitution.

2x – 3y = –2

4x + y = 24

The idea here is to solve one of the equations for one of the variables, and plug this into the other equation. It does not matter which equation or which variable you pick. There is no right or wrong choice; the answer will be the same, regardless. But — some choices may be better than others.

For instance, in this case, can you see that it would probably be simplest to solve the second equation for "y =", since there is already a y floating around loose in the middle there? I could solve the first equation for either variable, but I'd get fractions, and solving the second equation for x would also give me fractions. It wouldn't be "wrong" to make a different choice, but it would probably be more difficult. Being lazy, I'll solve the second equation for y:

4x + y = 24

y = –4x + 24

Now I'll plug this in ("substitute it") for "y" in the first equation, and solve for x:

2x – 3(–4x + 24) = –2

2x + 12x – 72 = –2

14x = 70

x = 5

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Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twe

alina1380 [7]

Just to remove ambiguities, the bar over the expression means it's repeating itself to infinity.

$\bf 2.888\overline{8}\impliedby \textit{now say, let's make }x=2.888\overline{8}
\\\\\\
\textit{and multiply it by 10, to move over the 8 to the left}
\\\\\\
\begin{array}{llll}
10x&=&10\cdot 2.888\overline{8}\\
&&28.88\overline{8}\\
&&26+2.888\overline{8}\\
&&26+x
\end{array}\implies 10x=26+x
\\\\\\
9x=26\implies x=\cfrac{26}{9}$

notice, the idea being, you multiply it by 10 at some power, so that you move the "recurring decimal" to the other side of the point, and then split it with a digit and "x".

now, you can plug that in your calculator, to check what you get.

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3 years ago

Read 2 more answers

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iVinArrow [24]

Answer:

Step-by-step explanation:

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2 years ago

According to the U.S. National Transportation Safety Board, the number of airline accidents by year from 1983 to 2006 were 23, 1

Lera25 [3.4K]

Answer:

$\bar X= 33.79167$

$s= 12.06497$

$SE= \frac{s}{\sqrt{n}}= \frac{12.06497}{\sqrt{24}}=2.463$

$Median= \frac{30+31}{2}= 30.5$

Step-by-step explanation:

For this case we have the following data:

23, 16, 21, 24, 34, 30, 28, 24, 26, 18, 23, 23, 36, 37, 49, 50, 51, 56, 46, 41, 54, 30, 40, and 31

We can calculate the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X= 33.79167$

Then we can calculate the standard deviation with this formula:

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s= 12.06497$

And the sample size for this case is n =24. We can calculate the standard error with this formula:

$SE= \frac{s}{\sqrt{n}}= \frac{12.06497}{\sqrt{24}}=2.463$

And the median for this case since the sample size is 24 first we need to sort the data on increasing order and we got:

16 18 21 23 23 23 24 24 26 28 30 30 31 34 36 37 40 41 46 49 50 51 54 56

And for this case the median would be the average from the position 12 and 13 and we got:

$Median= \frac{30+31}{2}= 30.5$

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3 years ago

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BartSMP [9]

Answer:

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3 years ago

If x varies inversely as y 2, and x = 2 when y = 20, find x when y = 5.

Dominik [7]

Step-by-step explanation:

$x = \frac{k}{y}$

x varies inversely as y. This means that x is equal to the inverse of y which can be translated as x = 1/y but the problem said that x is not exactly equal to the inverse of y. Therefore, we need to introduce a factor k. Factor k will represent the word "varies" in the problem.

To illustrate:

$x = \frac{k}{y}$

Since we don't have the value of k, we have to solve for it by using the first values of x and y which was given as x=2 and y=20.

$x = \frac{k}{y} \\ 2 = \frac{k}{20} \\ k = 2(20) = 40$

Now that we have the value of k, we can now solve for the value of x when y=5.

$x = \frac{k}{y} \\ = \frac{40}{5} \\ = 8$

Therefore, when y is 5, the value of x is 8.

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3 years ago