Question 175918
I'll do the first one to get you started





Start with the given system of equations:



{{{system(3x-5y=-9,5x-6y=-8)}}}



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



Let's graph the first equation:



{{{3x-5y=-9}}} Start with the first equation.



{{{-5y=-9-3x}}} Subtract {{{3x}}} from both sides.



{{{y=(-9-3x)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.



{{{y=(3/5)x+9/5}}} 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,(3/5)x+9/5)
)}}} Graph of {{{y=(3/5)x+9/5}}}.



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Now let's graph the second equation:



{{{5x-6y=-8}}} Start with the second equation.



{{{-6y=-8-5x}}} Subtract {{{5x}}} from both sides.



{{{y=(-8-5x)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{y}}}.



{{{y=(5/6)x+4/3}}} 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,(5/6)x+4/3)
)}}} Graph of {{{y=(5/6)x+4/3}}}.



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Now let's graph the two equations together:



{{{drawing(500,500,-10,10,-10,10,
grid(1),
graph(500,500,-10,10,-10,10,(3/5)x+9/5,(5/6)x+4/3)
)}}} Graph of {{{y=(3/5)x+9/5}}} (red). Graph of {{{y=(5/6)x+4/3}}} (green)



From the graph, we can see that the two lines intersect at the point *[Tex \LARGE \left(2,3\right)]. So the solution to the system of equations is *[Tex \LARGE \left(2,3\right)]. This tells us that the system of equations is consistent and independent.