Question

Which equation could be used to solve the following system?

Answer 1

Answer:

$x^2 + 66x -371 = 0$

Step-by-step explanation:

We have two equations:

x + y = 11                 (i)

$4x^2 - 3y^2 = 8$      (ii)

Clear x in equation (i) and substitute it in equation (ii)

$4x^2 -3(11-x)^2 = 8$

$4x^2 -3(121 -22x +x^2) = 8$

$4x^2 -363 + 66x - 3x^2 -8 = 0$

$x^2 + 66x -371 = 0$

To find the roots of this equation we use the quadratic formula

$\frac{-b +/- \sqrt{b^2 - 4ac}}{2a}$

Where:

b = 66

a = 1

c = -371

Then:

$\frac{-66 + \sqrt{66^2 - 4(1)(-371)}}{2(1)}\\\\and\\\\\frac{-66 - \sqrt{66^2 - 4(1)(-371)}}{2(1)}$

Then the solutions are:

$x = -33 + 2\sqrt{365} = 5.21$

and

$x = -33 - 2\sqrt{365} = -71.21$

Finaly, equation could be used to solve the system is $x^2 + 66x -371 = 0$