Final answer:
To solve the system of equations using the elimination method, add the two equations together and simplify. This will result in a quadratic equation in two variables. Use the quadratic formula to find the solutions.
Step-by-step explanation:
To solve the given system of equations using the elimination method, we can start by adding the two equations together. This will eliminate the y² term.
Adding the equations: (x - y² + 3) + (2x² + y² - 4) = 0
After simplifying, we get: 3x² - 2y² - x - 1 = 0
This is a quadratic equation in two variables. To find the solutions, we can use the quadratic formula.