Question

Given the system of equations:

x² + y² = 7
x² - y² = 2

Find the solution where x<0 and y<0. What are the values of x and y.

Answer 1

The solution to the system of equations where both x and y are negative is x = -√4.5 and y = -√2.5.

Step-by-step explanation:

To find the solution to the system of equations x² + y² = 7 and x² - y² = 2 where x and y are both negative, we can solve the system algebraically. First, add the equations to eliminate the y² term:

x² + y² + (x² - y²) = 7 + 2

2x² = 9

x² = 4.5

Since we are looking for x < 0, we take the negative square root: x = -√4.5. Then we substitute x back into one of the original equations to find y:

(-√4.5)² - y² = 2

4.5 - y² = 2

y² = 2.5

Again, since y < 0, y = -√2.5. Therefore, the solution is x = -√4.5 and y = -√2.5.