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