Question

How many solutions does the system have?

Answer 1

Answer:

A. Exactly one solution

Step-by-step explanation:

Solve the system of equations.

y = x + 1

y = 2x - 5

Substitute one equation into the other.

y = 2x - 5

x + 1 = 2x - 5

Subtract 2x from both sides.

-x + 1 = -5

Subtract 1 from both sides.

-x = -6

Multiply both sides by -1.

x = 6

Put it back into the other equation.

y = x + 1

y = 6 + 1

Add.

y = 7

The solution is (6, 7). Since the equations aren't equal, there are not infinitely many solutions, but since there is a solution found, we can determine that there is exactly one solution.