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Use the elimination method to find all solutions of the system of equations. {x-y²+3=0 {2 x²+y²-4=0

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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.

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