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2 votes
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

2 Answers

2 votes
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
User Pwyg
by
8.0k points
0 votes

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.

User Jwh
by
7.4k points

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