Question 161081


Start with the given system of equations:



{{{system(3x-y=17,3x+4y=7)}}}



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-y=17}}} Start with the first equation.



{{{-y=17-3x}}} Subtract {{{3x}}} from both sides.



{{{y=(17-3x)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=3x-17}}} 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,-10,10,3x-17)
)}}} Graph of {{{y=3x-17}}}.



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Now let's graph the second equation:



{{{3x+4y=7}}} Start with the second equation.



{{{4y=7-3x}}} Subtract {{{3x}}} from both sides.



{{{y=(7-3x)/(4)}}} Divide both sides by {{{4}}} to isolate {{{y}}}.



{{{y=-(3/4)x+7/4}}} 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,-(3/4)x+7/4)
)}}} Graph of {{{y=-(3/4)x+7/4}}}.



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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,-10,10,3x-17,-(3/4)x+7/4)
)}}} Graph of {{{y=3x-17}}} (red). Graph of {{{y=-(3/4)x+7/4}}} (green)



From the graph, we can see that the two lines intersect at the point *[Tex \LARGE \left(5,-2\right)]. So the solution to the system of equations is *[Tex \LARGE \left(5,-2\right)]. This tells us that the system of equations is consistent and independent.