SOLUTION: Hello, I need assistance with the following problem: Solve the following nonlinear system by elimination: {{{ 7x^2+11y^2=28 }}} {{{ x^2+y^2=4 }}} In advance, thanks so

Algebra ->  Systems-of-equations -> SOLUTION: Hello, I need assistance with the following problem: Solve the following nonlinear system by elimination: {{{ 7x^2+11y^2=28 }}} {{{ x^2+y^2=4 }}} In advance, thanks so       Log On


   

Question 6845: Hello, I need assistance with the following problem:

Solve the following nonlinear system by elimination:
+7x%5E2%2B11y%5E2=28+
+x%5E2%2By%5E2=4+

In advance, thanks so much for your assistance!!!
Answer by prabhjyot(165) About Me  (Show Source):
You can put this solution on YOUR website!
+7x%5E2%2B11y%5E2=28+ ---->(1)
+x%5E2%2By%5E2=4+ --->(2)
This time we have an ellipse and a hyperbola. Neither one are in standard form however
if we just add the two equations we will eliminate the y’s from the system
for that multiply equation(2) by -11 we get
-11x%5E2+-11y%5E2+=-44 --->(3)
Now adding equation (1) and equation(3) we get
+7x%5E2++%2B11y%5E2++=++28
-11x%5E2+-11y%5E2++=+-44
---------------------
-4x%5E2++++%2B0++++=+-16
solve for x.
-4x%5E2+=+-16
x%5E2+=+16%2F4+=+4
x%5E2=4
x=+sqrt%284%29+=2
x= +/-2
To determine the value(s) of the y’s we can substitute these into either of the equations.
x=2
7x%5E2++%2B11y%5E2++=++28
7%282%29%5E2+%2B11y%5E2+=28
28+%2B11y%5E2+=28

y%5E2+=0
y=0
x=-2
7%28-2%29%5E2+%2B11y%5E2+=28
y=0
Therefore the solutions are :(2,0) (-2,0)