Question

How many solutions does the system have?

x = -4y + 4
2x + 8y = 8

A. one solution
B. two solutions
C. infinitely many solutions
D. no solution

Answer 1

1st equation
x = -4y + 4 

2nd equation
2x + 8y = 8 
  x + 4y = 4
x = -4y + 4

so
-4y + 4 =-4y + 4
0 = 0

then
there's many solutions

answer
C. infinitely many solutions 

Answer 2

Answer:  The correct option is

(C) Infinitely many solutions.

Step-by-step explanation:  We are given to find the number of solutions that the following system of equations have :

$x=-4y+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x+8y=8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of x from equation (i) in equation (ii), we get

$2x+8y=8\\\\\Rightarrow 2(-4y+4)+8y=8\\\\\Rightarrow -8y+8+8y=8\\\\\Rightarrow 8=8,$

which is always true.

Thus, the given system of equations have infinite number of solutions.

Option (C) is CORRECT.