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

Question

asked Mar 11, 2017 207k views

2 Answers

Renanleandrof · Answer 1 · 2017-03-17T10:56:56+0000

Answer

Find out the solution to the system of equations .

To prove

As the equations are

y = x – 10 , 4 = 2xy

$Put\ y = (4)/(2x)$

in the equation y = x – 10

(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

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

$x = 10\pm (√(100+ 8))/(2)$

$x = 5\pm (√(108))/(2)$

$x = 5\pm (6√(3))/(2)$

$x = 5\pm 3√(3)$

Thus the solution are

$x = 5\ + 3√(3)$

Put in the 4 = 2xy

y = (4)/(2(5+3√(3) ))

y = (2)/((5+3√(3) ))

When

$x = 5\ - 3√(3)$

Put in the 4 = 2xy

y = (4)/(2(5 -3√(3) ))

y = (2)/((5 - 3√(3) ))