Question 111981
Start with the given system

{{{8x-4y=16}}}
{{{y=2x-4}}}




{{{8x-4(2x-4)=16}}}  Plug in {{{y=2x-4}}} into the first equation. In other words, replace each {{{y}}} with {{{2x-4}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{8x-8x+16=16}}} Distribute



{{{16=16}}} Combine like terms on the left side



{{{0=16-16}}}Subtract 16 from both sides



{{{0=0}}} Combine like terms on the right side



Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.