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3 years ago

If 2x +y=8, x+2y=4, find the value of x-y. Please, help me

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

y = 8 -2x

x + 2 (8 - 2x) = 1

x + 16 - 4x = 1

x - 4x = -15

-3x = -15

x = 5

If x = 5, then we can substitute in...

5 + 2y = 1

2y = -4

y = -2

Now let us check that by substituting those values in to the equation

2x + y = 8

2 (5) + (-2) = 8

That is correct so we have the right values for x and y/

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Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.

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Answer:

Step-by-step explanation:

Suppose we a point $P(x,y,z)$ such that its distance from either the point $A(3,4,-5)$ or $B(-2,1,4)$ is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

$r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}$

$AP = \sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2}$

similarly, we can find the distance BP

$BP = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

since both distances are exactly the same we can equate them

$AP = BP$

$\sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2} = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

$(3 - x)^2 + (4 - y)^2 + (-5 - z)^2 = (-2 - x)^2 + (1 - y)^2 + (4 - z)^2$

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

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Step-by-step explanation:

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