Question 166684
Start with the given system

{{{2x-7y=8}}}
{{{x=(7/2)y+4}}}




{{{2((7/2)y+4)-7y=8}}}  Plug in {{{x=(7/2)y+4}}} into the first equation. In other words, replace each {{{x}}} with {{{7/2y+4}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{2((7/2)y)+2(4)-7y=8}}} Distribute



{{{7y+8-7y=8}}} Multiply



{{{0y+8=8}}} Combine like terms on the left side.



{{{0y=8-8}}} Subtract {{{8}}} from both sides.



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



{{{0=0}}} Simplify.



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