Question 197357
Start with the given system

{{{2x+5y=3}}}
{{{x=9-5y}}}




{{{2(9-5y)+5y=3}}}  Plug in {{{x=9-5y}}} into the first equation. In other words, replace each {{{x}}} with {{{9-5y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{18-10y+5y=3}}} Distribute



{{{-5y+18=3}}} Combine like terms on the left side



{{{-5y=3-18}}}Subtract 18 from both sides



{{{-5y=-15}}} Combine like terms on the right side



{{{y=(-15)/(-5)}}} Divide both sides by -5 to isolate y




{{{y=3}}} Divide





Now that we know that {{{y=3}}}, we can plug this into {{{x=9-5y}}} to find {{{x}}}




{{{x=9-5(3)}}} Substitute {{{3}}} for each {{{y}}}



{{{x=9-15}}} Multiply



{{{x=-6}}} Subtract



So our answers are {{{x=-6}}} and {{{y=3}}} which form the ordered pair *[Tex \LARGE \left(-6,3\right)]