Question 120508

Start with the given system

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




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



{{{4x-8-4x=-8}}} Distribute



{{{-8=-8}}} Combine like terms on the left side



{{{0=-8+8}}}Add 8 to both sides



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



{{{0=0}}} Simplify


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.