Question 149513

Start with the given system

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




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



{{{4x+4-4x=4}}} Distribute



{{{4=4}}} Combine like terms on the left side



{{{0=4-4}}}Subtract 4 from both sides



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



Since this equation is <font size=4><b>always</b></font> true for any x value, this means x can equal any number. So there are an infinite number of solutions.