Answer:
Option C. [tex]y=-\frac{1}{2}(2x-8)[/tex]
Step-by-step explanation:
we know that
If a system of two linear equations has an infinite number of solutions, then both equations must be identical
The given equation is
[tex]y=-x+4[/tex]
Verify each case
Option A. we have
[tex]y=-4(x+1)[/tex]
apply distributive property
[tex]y=-4x-4[/tex]
Compare with the given equation
[tex]-x+4 \neq -4x-4[/tex]
Option B. we have
[tex]y=-(x+4)[/tex]
remove the parenthesis
[tex]y=-x-4[/tex]
Compare with the given equation
[tex]-x+4 \neq -x-4[/tex]
Option C. we have
[tex]y=-\frac{1}{2}(2x-8)[/tex]
apply distributive property
[tex]y=-x+4[/tex]
Compare with the given equation
[tex]-x+4=-x+4[/tex]
therefore
This equation with the given equation form a system that has an infinite number of solutions
Option D. we have
[tex]y=x+4[/tex]
Compare with the given equation
[tex]-x+4 \neq x+4[/tex]
