Question 115284

Start with the given system

{{{6x-3y=3}}}
{{{y=3x-5}}}




{{{6x-3(3x-5)=3}}}  Plug in {{{y=3x-5}}} into the first equation. In other words, replace each {{{y}}} with {{{3x-5}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{6x-9x+15=3}}} Distribute



{{{-3x+15=3}}} Combine like terms on the left side



{{{-3x=3-15}}}Subtract 15 from both sides



{{{-3x=-12}}} Combine like terms on the right side



{{{x=(-12)/(-3)}}} Divide both sides by -3 to isolate x




{{{x=4}}} Divide





Now that we know that {{{x=4}}}, we can plug this into {{{y=3x-5}}} to find {{{y}}}




{{{y=3(4)-5}}} Substitute {{{4}}} for each {{{x}}}



{{{y=7}}} Simplify



So our answer is {{{x=4}}} and {{{y=7}}}