Question

Solve the system of equations by elimination:
x² - y² = 3
2x² + y² = 6

Answer 1

To solve the system of equations by elimination, add the two equations together to eliminate the y terms. Divide both sides by 2 and take the square root to find the value of x. Substitute the value of x into one of the original equations to solve for y.

Step-by-step explanation:

To solve the given system of equations by elimination, we can add the two equations together to eliminate the y terms. This will give us:

x² - y² + (x² + y²) = 32 + 6

Simplifying this equation gives us:

2x² = 38

Dividing both sides by 2, we find:

x² = 19

Taking the square root of both sides, we get:

x = ±√19

So the solutions to the system of equations are:

x = √19, y = -√13

or

x = -√19, y = √13