Final answer:
To solve the system of equations using the elimination method, multiply the second equation by -1, add it to the first equation, and solve for x. Then substitute the value of x back into either of the original equations to solve for y. The solutions are (-2, √3) and (-2, -√3).
Step-by-step explanation:
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. Let's start by multiplying the second equation by -1. This will give us -2x² + y² = -x - 3. Now we can add this equation to the first equation, which eliminates the x² term. We are left with 0 = -x - 2. Solving for x gives us x = -2.
Now we can substitute this value of x into either of the original equations to find the corresponding value of y. Using the first equation, we have (-2)² - y² = 1. Simplifying, we get 4 - y² = 1. Rearranging this equation gives us y² = 3. Taking the square root of both sides gives us y = ±√3.
So the solutions to the system of equations are (-2, √3) and (-2, -√3).