Question 123357

Start with the given system

{{{10x+2y=7}}}
{{{y=-5x+3}}}




{{{10x+2(-5x+3)=7}}}  Plug in {{{y=-5x+3}}} into the first equation. In other words, replace each {{{y}}} with {{{-5x+3}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{10x+-10x+6=7}}} Distribute



{{{6=7}}} Combine like terms on the left side



{{{0=7-6}}}Subtract 6 from both sides



{{{0=1}}} Combine like terms on the right side



{{{0=1}}} Simplify


Since this equation is <font size=4><b>never</b></font> true for any x value, this means there are no solutions.