How many solutions does the

Question

following system of equations have?

x + y = −9
−x − y = 9

Answer 1

This system of equations has an infinite number of solutions.

Adding the two equations together, we get:

x + y + (-x - y) = -9 + 9
0 = 0

This equation is always true, meaning that the two original equations are essentially the same. Therefore, any values of x and y that satisfy one of the equations will satisfy the other equation as well. This means there are infinitely many solutions to this system of equations.