<PRE><B>Question 243528</B>

Start with the given system of equations:

{{{system(x+3y=14,-x+7y=6)}}}



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)+(-x+7y)=(14)+(6)}}}



{{{(x-x)+(3y+7y)=14+6}}} Group like terms.



{{{0x+10y=20}}} Combine like terms.



{{{10y=20}}} Simplify.



{{{y=(20)/(10)}}} Divide both sides by {{{10}}} to isolate {{{y}}}.



{{{y=2}}} Reduce.



------------------------------------------------------------------



{{{x+3y=14}}} Now go back to the first equation.



{{{x+3(2)=14}}} Plug in {{{y=2}}}.



{{{x+6=14}}} Multiply.



{{{x=14-6}}} Subtract {{{6}}} from both sides.



{{{x=8}}} Combine like terms on the right side.



So the solutions are {{{x=8}}} and {{{y=2}}}.



Which form the ordered pair *[Tex \LARGE \left(8,2\right)].



This means that the system is consistent and independent.



Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(8,2\right)]. So this visually verifies our answer.



{{{drawing(500,500,-2,18,-8,12,
grid(1),
graph(500,500,-2,18,-8,12,(14-x)/(3),(6+x)/(7)),
circle(8,2,0.05),
circle(8,2,0.08),
circle(8,2,0.10)
)}}} Graph of {{{x+3y=14}}} (red) and {{{-x+7y=6}}} (green) 

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