Question

You are given the following system of equations. Without graphing or performing any substitutions, can you see how many real solutions the system must have? Describe your reasoning.

y=x
y = - 1
Ws
Choose the correct answer below.
OA. There must be exactly one solution because the second equation just gives the value for y.
OB. There must be no real solutions since the first equation can only be true for nonnegative y-values, but the second equation gives a negative y-value
OC. There must be infinitely many solutions because there the system is true for any value of x.
D. There must be two solutions because linear-quadratic systems of equations always have two solutions.

Answer 1

The correct answer is Option A. The system of equations y = x and y = -1 has exactly one solution, which is x = -1 and y = -1.

Step-by-step explanation:

If we are given the system of equations y = x and y = -1, we can determine the number of real solutions without graphing or performing any substitutions. Since the second equation directly specifies that y must be -1, any solution must satisfy this condition. Substituting y with -1 in the first equation, we get -1 = x. This means there is exactly one solution to this system: x = -1 and y = -1. Therefore, the correct answer is OA.