Question 132477
Start with the given system

{{{-3x+3y=15}}}
{{{y=x+5}}}




{{{-3x+3(x+5)=15}}}  Plug in {{{y=x+5}}} into the first equation. In other words, replace each {{{y}}} with {{{x+5}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{-3x+3x+15=15}}} Distribute



{{{15=15}}} Combine like terms on the left side



{{{0=15-15}}}Subtract 15 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.