Question

what is the solution to the system of equations? y = x – 10 2x y = 4

Answer 1

Answer

Find out the  solution to the system of equations .

To prove

As the equations are

y = x – 10 , 4 = 2xy

$Put\ y = \frac{4}{2x}$

in  the equation  y = x – 10

$\frac{4}{2x} = x - 10$

Than the equation becomes

2x² - 20x - 4 = 0

Taking 2 as common

x² - 10x - 2 = 0

Now using the discriment formula

$D = -b\pm \frac{\sqrt{b^{2} - 4ac}}{2a}$

Here a = 1 , b = -10 , c = -2

Put in the above

$x = 10\pm \frac{\sqrt{(-10)^{2} - 4\times 1\times -2}}{2}$

$x = 10\pm \frac{\sqrt{100+ 8}}{2}$

$x = 5\pm \frac{\sqrt{108}}{2}$

$x = 5\pm \frac{6\sqrt{3}}{2}$

$x = 5\pm 3\sqrt{3}$

Thus the solution are

$x = 5\ + 3\sqrt{3}$

Put in the  4 = 2xy

$y = \frac{4}{2(5+3\sqrt{3} )}$

$y = \frac{2}{(5+3\sqrt{3} )}$

When

$x = 5\ - 3\sqrt{3}$

Put in the  4 = 2xy

$y = \frac{4}{2(5 -3\sqrt{3} )}$

$y = \frac{2}{(5 - 3\sqrt{3} )}$

 

Answer 2

Answer:

C is the answer

Step-by-step explanation:

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