Question 188803
I'm assuming that you want to solve this system by graphing.





Start with the given system of equations:



{{{system(-6x+6y=6,-6x+3y=-12)}}}



In order to graph these equations, we <font size="4"><b>must</b></font> solve for y first.



Let's graph the first equation:



{{{-6x+6y=6}}} Start with the first equation.



{{{6y=6+6x}}} Add {{{6x}}} to both sides.



{{{y=(6+6x)/(6)}}} Divide both sides by {{{6}}} to isolate {{{y}}}.



{{{y=x+1}}} Rearrange the terms and simplify.



Now let's graph the equation:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,x+1)
)}}} Graph of {{{y=x+1}}}.



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Now let's graph the second equation:



{{{-6x+3y=-12}}} Start with the second equation.



{{{3y=-12+6x}}} Add {{{6x}}} to both sides.



{{{y=(-12+6x)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



{{{y=2x-4}}} Rearrange the terms and simplify.



Now let's graph the equation:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,2x-4)
)}}} Graph of {{{y=2x-4}}}.



-------------------------------------------------------------------



Now let's graph the two equations together:



{{{drawing(500,500,-10,10,-10,10,
grid(1),
graph(500,500,-10,10,-10,10,x+1,2x-4)
)}}} Graph of {{{y=x+1}}} (red). Graph of {{{y=2x-4}}} (green)



From the graph, we can see that the two lines intersect at the point *[Tex \LARGE \left(5,6\right)]. So the solution to the system of equations is *[Tex \LARGE \left(5,6\right)]. This tells us that the system of equations is consistent and independent.