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4 years ago

15

Find the solution of the system of equations 2x-4y=32 2x-8y=48

2 answers:

Sveta_85 [38]4 years ago

6 0

<span>2x-4y=32
2x-8y=48
--------------subtract
4y = - 16
y = -4

</span>2x-4y=32
2x- 4(-4)=32
2x + 16 = 32
2x = 16
x = 8

answer
(8, -4)

erastovalidia [21]4 years ago

4 0

2x - 4y = 32
2x - 8y = 48

Multiple equation 2 by -1 so the 'x' variables will cancel.
-1(2x - 4y = 32)
-2x + 4y = - 32
2x - 8y = 48
-------------------- add
- 4y = 16 divide both sides by -4
y = -4
Plug -4 back into either equation and solve for y.
2x - 4y = 32
2x -4(-4) = 32
2x + 16 = 32 subtract 16 from both sides
2x = 16 divide both sides by 2
x = 8
(8, -4)

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$f(x)=(x-2)(x+3)(x-1)^2$ .

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According to rational roots theorem,

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This implies that

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$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

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We can see from the factorization that the roots

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Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

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$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

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