What is the solution of the system?

use the substitution method.

{y−2x=8
{16+4x=2y

the only solution is (24, 0)

the only solution is (1, 10)

there is no solution.

there are an infinite number of solutions.

Subsitution

solve for y in first equation
add 2x to both sides
y=2x+8
sub 2x+8 for y in second equation
16+4x=2(2x+8)
divide both sides by 2
8+2x=2x+8
true
there are infinite solutions for x
therefor infinite soltions for y

there are an infinite number of solutions