Question 144716



Start with the given system of equations:


{{{system(x+5y=4,2x-5y=2)}}}





{{{2(x+5y)=2(4)}}}  Multiply the top equation (both sides) by {{{2}}}
{{{-1(2x-5y)=-1(2)}}}  Multiply the bottom equation (both sides) by {{{-1}}}





Distribute and multiply


{{{2x+10y=8}}}
{{{-2x+5y=-2}}}



Now add the equations together. In order to add 2 equations, group like terms and combine them


{{{(2x-2x)+(10y+5y)=8-2}}}


Combine like terms and simplify




{{{cross(2x-2x)+15y=6}}} Notice how the x terms cancel out





{{{15y=6}}} Simplify





{{{y=6/15}}} Divide both sides by {{{15}}} to isolate y





{{{y=2/5}}} Reduce




Now plug this answer into the top equation {{{x+5y=4}}} to solve for x


{{{x+5y=4}}} Start with the first equation




{{{x+5(2/5)=4}}} Plug in {{{y=2/5}}}





{{{x+10/5=4}}} Multiply





{{{x+2=4}}} Reduce




{{{x=4-2}}}Subtract 2 from both sides



{{{x=2}}} Combine like terms on the right side





So our answer is

{{{x=2}}} and {{{y=2/5}}}




which form the ordered pair *[Tex \LARGE \left(2,\frac{2}{5}\right)]