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xxTIMURxx [149]

3 years ago

6

Evaluate Dx -4x+7y=1 25=2x+5y

1 answer:

user100 [1]3 years ago

8 0

Equation 1) -4x + 7y = 1
Equation 2) 25 = 2x + 5y

For both equations, move the variables all onto one side, preferably the left side.

To do so, for equation 2, subtract 2x from both sides, as well as subtracting 5y from both sides, and then subtracting 25 from both sides.

2) -2x - 5y = -25
1) -4x + 7y = 1

Multiply all of equation 2 by 2.

2) 2(-2x - 5y = -25)

2) -4x - 10y = -50
1) -4x + 7y = 1

Subtract the equations from each other.

-17y = -51

Divide both sides by -17.

y = 51/17

y = 3

Plug in 3 for y in the first equation.

-4x + 7y = 1

-4x + 7(3) = 1

-4x + 21 = 1

-4x = 1 - 21

-4x = -25

x = -25/-4

x = 25/4

x = 6 1/4

(6 1/4, 3)

~Hope I helped!~

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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

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

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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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