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Liula [17]
3 years ago
15

-2x+2y=6 7x-8y=-27 what is the solution

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0
-2x+2y=6
7x-8y=-27
5x-6y=-21
-x+y=3
6x-7y=-24
6x-7y=-4(-2x+2y)
6x-7y=8x-8y
-6x from both sides:
-7y=2x-8y
add 8y to both sides:
y=2x
-2x+2y=6
2y-6=2x
2y-6=-12
-6-6=-12
y=-3
x=-6

Hope this helps :)

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Help
kobusy [5.1K]

The equation of the line is y - 3 = 5(x - 8) ⇒ c

Step-by-step explanation:

The point-slope form of the linear equation is y-y_{1}=m(x-x_{1}) , where:

  • m is the slope of the line
  • (x_{1},y_{1}) is a point on the line

∵ The line passes through point (8 , 3)

∴ x_{1} = 8 and y_{1} = 3

∵ The slope of the line is 5

∴ m = 5

- Substitute these values in the form of the equation below

∵ y-y_{1}=m(x-x_{1})

∴ y - 3 = 5(x - 8)

The equation of the line is y - 3 = 5(x - 8)

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

#LearnwithBrainly

3 0
3 years ago
What is the slope of the following equation?
777dan777 [17]

Answer: A. -3

Step-by-step explanation: The slope is the coefficent of x, this can be read as -3/1, down 3 over 1.

6 0
2 years ago
I need help please?!!!
malfutka [58]

a<-28 I think. Can I have a Brainliest

6 0
3 years ago
Read 2 more answers
Answers for the homies that don’t wanna do the work edge 202
trapecia [35]
Wait what’s edge 202:|
7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \
Kisachek [45]

Answer:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2

Step-by-step explanation:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} = \ ?

We can use Part I of the Fundamental Theorem of Calculus:

  • \displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

  • \displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt}\  = -\int\limits^a_b \text{f(t) dt}

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

  • \displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx}  \int\limits^{x^2}_0 t^2+1 \text{ dt}  

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

  • \displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]
  • where u represents any function other than a variable

For the first term, replace \text{t} with 2x, and apply the chain rule to the function. Do the same for the second term; replace

  • \displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)  

Simplify the expression by distributing 2 and 2x inside their respective parentheses.

  • [-(8x^2 +2)] + (2x^5 + 2x)
  • -8x^2 -2 + 2x^5 + 2x

Rearrange the terms to be in order from the highest degree to the lowest degree.

  • \displaystyle2x^5-8x^2+2x-2

This is the derivative of the given integral, and thus the solution to the problem.

6 0
2 years ago
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