Determine the number of solutions to the system of linear equations (0, 1, infinite symbol):
y=7x+8
-7x+y=-8
This system of linear equations is consistent and dependent, meaning there are infinite solutions.
To see this, let's solve the system:
From the first equation, we can write y = 7x + 8.
Substituting this into the second equation, we have:
-7x + (7x + 8) = -8
Simplifying, we get:
7x - 7x + 8 = -8
8 = -8
This is a contradiction, and therefore there is no unique solution.
Since the system is consistent (meaning a solution exists) but the equations are dependent (meaning they are not unique), there are infinite solutions.