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3 years ago

Solve the system of linear equations by elimination 2x+7y=1 2x-4y=12

1 answer:

3 0

$\left\{\begin{array}{ccc}2x+7y=1\\2x-4y=12&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+7y=1\\-2x+4y=-12\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad11y=-11\qquad\text{divide both sides by 11}\\.\qquad\qquad \boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\2x+7(-1)=1\\2x-7=1\qquad\text{add 7 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\Answer:\ \boxed{x=4\ and\ y=-1\to(4,\ -1)}$

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JulsSmile [24]

Answer:

The linear regression equation that represents the set of data is:

$y=1083.48+23.73x$

The predicted number of new cases for 2013 is 1368.

Step-by-step explanation:

The general form of a linear regression is:

$y=a+bx$

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

Compute the values of a and b as follows:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6857 \cdot 55 - 15 \cdot 17558}{ 6 \cdot 55 - 15^2} \approx 1083.476 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 17558 - 15 \cdot 6857 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 23.743\end{aligned}$

The linear regression equation that represents the set of data is:

$y=1083.48+23.73x$

Compute the predicted value of the number of new cases for 2013 (i.e. x = 12) as follows:

$y=1083.48+23.73x$

$=1083.48+(23.73\times12)\\\\=1083.48+284.76\\\\=1368.24\\\\\approx 1368$

Thus, the predicted number of new cases for 2013 is 1368.

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3 years ago

When the sum of a number and 3 is subtracted from 10 the result is 5. What is the integer

Rashid [163]

In algebraic terms this is:

$10-(x+3)=5\\10-x-3=5\\10-x=5+3\\10-x=8\\-x=8-10\\-x=-2\\x=2$

The integer is 2.

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2 years ago

Find the solution of the square root of the quantity of x plus 2 plus 4 equals 8, and determine if it is an extraneous solution

Iteru [2.4K]

Consider the equation:

$\sqrt{x+2}+4 = 8$

Subtracting '4' from both the sides of the equation, we get as

$\sqrt{x+2}+4-4= 8-4$

$\sqrt{x+2}= 4$

Squaring on both the sides of the equation, we get

$(\sqrt{x+2})^2 = (4)^2$

$x+2 = 16$

Subtracting '2' from both the sides of the equation, we get

$x+2-2=16-2$

x=14

Since, An extraneous solution is a solution that arises from the solving process that is not really a solution at all. But, in this equation x=14 is the solution of the given equation.

Hence, it is not an extraneous solution.

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