Question 154784


Start with the given system of equations:

{{{system(x+3y=3,2x+3y=4)}}}



{{{-1(2x+3y)=-1(4)}}} Multiply the both sides of the second equation by -1.



{{{-2x-3y=-4}}} Distribute and multiply.



So we have the new system of equations:

{{{system(x+3y=3,-2x-3y=-4)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(x+3y)+(-2x-3y)=(3)+(-4)}}}



{{{(1x+-2x)+(3y+-3y)=3+-4}}} Group like terms.



{{{-x+0y=-1}}} Combine like terms. Notice how the y terms cancel out.



{{{-x=-1}}} Simplify.



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



{{{x=1}}} Reduce.



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{{{x+3y=3}}} Now go back to the first equation.



{{{1+3y=3}}} Plug in {{{x=1}}}.



{{{1+3y=3}}} Multiply.



{{{3y=3-1}}} Subtract {{{1}}} from both sides.



{{{3y=2}}} Combine like terms on the right side.



{{{y=(2)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



So our answer is {{{x=1}}} and {{{y=2/3}}}.



Which form the ordered pair *[Tex \LARGE \left(1,\frac{2}{3}\right)].



This means that the system is consistent and independent.