Question

Systems Of Nonlinear Equations

-Solve the following equations.

1. { x+2y=0

{ x²+y²=5

2. { x+y=3

{ x²+y²=2

Answer 1

1.

$$\begin{cases} x=-2y\\ (-2y)^2+y^2=5 \end{cases}$$

$$\begin{cases} x=-2y\\ 5y^2=5 \end{cases}$$

$$\begin{cases} x=-2y\\ y^2=1 \end{cases}$$

$$\begin{cases} x=2\\ y=-1 \end{cases}\text{ or }\begin{cases} x=-2\\ y=1 \end{cases}$$

$(-2, 1), (2, -1)$

2.

$$\begin{cases} x=3-y\\ (3-y)^2+y^2=2 \end{cases}$$

$$\begin{cases} x=3-y\\ 9-6y+y^2+y^2=2 \end{cases}$$

$$\begin{cases} x=3-y\\ 2y^2-6y+7=0 \end{cases}$$

$D=(-6)^2-4(2)(7)=-20<0$

The system has no real solution.