Answer:
[tex]x^2 + 66x -371 = 0[/tex]
Step-by-step explanation:
We have two equations:
x + y = 11 (i)
[tex]4x^2 - 3y^2 = 8[/tex] (ii)
Clear x in equation (i) and substitute it in equation (ii)
[tex]4x^2 -3(11-x)^2 = 8[/tex]
[tex]4x^2 -3(121 -22x +x^2) = 8[/tex]
[tex]4x^2 -363 + 66x - 3x^2 -8 = 0[/tex]
[tex]x^2 + 66x -371 = 0[/tex]
To find the roots of this equation we use the quadratic formula
[tex]\frac{-b +/- \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
b = 66
a = 1
c = -371
Then:
[tex]\frac{-66 + \sqrt{66^2 - 4(1)(-371)}}{2(1)}\\\\and\\\\\frac{-66 - \sqrt{66^2 - 4(1)(-371)}}{2(1)}[/tex]
Then the solutions are:
[tex]x = -33 + 2\sqrt{365} = 5.21[/tex]
and
[tex]x = -33 - 2\sqrt{365} = -71.21[/tex]
Finaly, equation could be used to solve the system is [tex]x^2 + 66x -371 = 0[/tex]
