Question 393058
{{{2x+3y=0}}} Start with the second equation.



{{{2x+3(3x+3)=0}}}  Plug in {{{y=3x+3}}} into the first equation. In other words, replace each {{{y}}} with {{{3x+3}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{2x+9x+9=0}}} Distribute



{{{11x+9=0}}} Combine like terms on the left side



{{{11x=0-9}}}Subtract 9 from both sides



{{{11x=-9}}} Combine like terms on the right side



{{{x=(-9)/(11)}}} Divide both sides by 11 to isolate x




{{{x=-9/11}}} Reduce





Now that we know that {{{x=-9/11}}}, we can plug this into {{{y=3x+3}}} to find {{{y}}}



{{{y=3x+3}}} Start with the first equation.



{{{y=3(-9/11)+3}}} Substitute {{{-9/11}}} for each {{{x}}}



{{{y=-27/11+3}}} Multiply



{{{y=6/11}}} Add



So the solutions are {{{x=-9/11}}} and {{{y=6/11}}}



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