Question 112108
Start with the given system

{{{x-y=7}}}
{{{y=2x-10}}}




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



{{{x-2x+10=7}}} Distribute



{{{-x+10=7}}} Combine like terms on the left side



{{{-x=7-10}}}Subtract 10 from both sides



{{{-x=-3}}} Combine like terms on the right side



{{{x=(-3)/(-1)}}} Divide both sides by -1 to isolate x




{{{x=3}}} Divide





Now that we know that {{{x=3}}}, we can plug this into {{{y=2x-10}}} to find {{{y}}}




{{{y=2(3)-10}}} Substitute {{{3}}} for each {{{x}}}



{{{y=-4}}} Simplify



So our answer is {{{x=3}}} and {{{y=-4}}}