SOLVE THE NONLINEAR SYSTEM OF EQUATIONS FOR REAL SOLUTION

^{{}x

^{2 + 2 }y

^{2}= 2

x - y = 2

a) The solution is ??????

b) there is no solution

SOLVE THE NONLINEAR SYSTEM OF EQUATIONS FOR REAL SOLUTION

x - y = 2

a) The solution is ??????

b) there is no solution

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Houston, TX

Hi, Mario!

Is the system supposed to be the following?

x^{2} + 2y^{2} = 2

x - y = 2

If so, graphing the system shows an ellipse with a line outside of it; they do not intersect, therefore no solution.

To solve it algebraically, solve the linear equation for either variable: x = y + 2

Substitute y+2 into the first equation:

(y + 2)^{2} + 2y^{2} = 2

y^{2} + 4y + 4 + 2y^{2} = 2

3y^{2} + 4y + 2 = 0

Using the quadratic formula results in a negative number under the square root sign; therefore, there is no real number solution.

Hope this helps!

Kathye P.

Ansonia, CT

No solution as written; the first is an ellipse, the second a line, and they don't intersect.

Using substitution you can generate 3y^{2} + 4y + 2 = 0, which has no real roots. There are imaginary (complex, actually) roots where

y = (1/3)(-2 ± i√2)

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