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3 years ago

Use the elimination method to solve the system of equations? 6x+2y=8 12x+y=22

Mathematics

1 answer:

Xelga [282]3 years ago

3 0

The solution is: x=2, y=-2

Step-by-step explanation:

Given equations are:

6x+2y=8 Eqn 1

12x+y=22 Eqn 2

Multiplying Eqn 1 by 2

$2(6x+2y)=2(8)\\12x+4y=16$ Eqn 3

Subtracting Equation 2 from eqn 3

$12x+4y-(12x+y)=16-22\\12x+4y-12x-y=-6\\3y=-6\\Dividing\ both\ sides\ by\ 3\\\frac{3y}{3}=\frac{-6}{3}\\y=-2$

Putting y=-2 in eqn 2

$12x-2=22\\Adding\ 2\ on\ both\ sides\\12x-2+2=22+2\\12x=24\\Dividing\ both\ sides\ by\ 12\\\frac{12x}{12} = \frac{24}{2}\\x=2$

The solution is: x=2, y=-2

Keywords: Linear equations, Elimination Method

Learn more about elimination method at:

#LearnwithBrainly

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3 years ago

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Sedbober [7]

Answer:

The slope of the equation is -3.

Step-by-step explanation:

Given : Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each minute.

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Solution :

Let x be the number of minutes taken to dig the ground.

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3 years ago

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First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

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3 years ago

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Sholpan [36]

Answer:

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Step-by-step explanation:

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