Help with math

Question

SOLVE THE NONLINEAR SYSTEM OF EQUATIONS FOR REAL SOLUTION

 

^{ x^{2 + 2} y² = 2

   x   -   y  = 2

 

 

a) The solution is ??????  

 

b) there is no solution

 

Answer 1

Hi, Mario!

 

Is the system supposed to be the following?

 

x² + 2y² = 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 + 2y² = 2

y² + 4y + 4 + 2y² = 2

3y² + 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.

Answer 2

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

 

Using substitution you can generate 3y² + 4y + 2 = 0, which has no real roots. There are imaginary (complex, actually) roots where

 

y = (1/3)(-2 ± i√2)