How do you solve the system #9x^2+4y^2=36# and #-x+y=-4#?

1 Answer
Sep 30, 2016

Substitute #x - 4# for y in #9x^2 + 4y^2 = 36# to discover that there are no real roots for the resulting quadratic, therefore, the line does not intersect with the ellipse.

Explanation:

Given:
#y = x - 4#
#9x^2 + 4y^2 = 36#

#9x^2 + 4(x - 4)^2 = 36#

#9x^2 + 4(x^2 - 8x + 16) = 36#

#13x^2 - 32x + 64 = 36#

#13x^2 - 32x + 28 = 0#

#b^2 - 4(a)(c) = (-32)^2 - 4(13)(28) = -432#

There are no real roots, therefore, the line does not intersect with the ellipse