Question 157502

Start with the given system of equations:



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



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=-3}}} Start with the first equation.



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



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



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



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Now let's graph the second equation:



{{{2x+y=2}}} Start with the second equation.



{{{y=2-2x}}} Subtract {{{2x}}} from both sides.



{{{y=-2x+2}}} 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+2)
)}}} Graph of {{{y=-2x+2}}}.



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Now let's graph the two equations together:



{{{drawing(500,500,-5,5,-5,5,
grid(1),
graph(500,500,-5,5,-5,5,-3x+3,-2x+2)
)}}} Graph of {{{y=-3x+3}}} (red). Graph of {{{y=-2x+2}}} (green)



From the graph, we can see that the two lines intersect at the point *[Tex \LARGE \left(1,0\right)]. So the solution to the system of equations is *[Tex \LARGE \left(1,0\right)]. This tells us that the system of equations is consistent and independent.