How many solutions does the system of equations have?

x=-4y+4 and 2x+8y=8
A. one
B. two
C. infinitely many
D. none

infinity

Thanks

To determine the number of solutions for the system of equations, we can solve the equations simultaneously.

Let's start by rearranging the first equation to solve for x:
x = -4y + 4

Now substitute this value for x in the second equation:
2(-4y+4) + 8y = 8

Simplify the equation:
-8y + 8 + 8y = 8
0 = 0

The resulting equation, 0 = 0, indicates that both variables y and x have been eliminated and are therefore not independent. This means that the two original equations represent the same line, and they are equivalent. Consequently, the system of equations has infinitely many solutions.

Therefore, the correct answer is C. infinitely many.