Question 165449


Start with the given system of equations:



{{{system(x+y=3,x+y=-1)}}}



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



Let's graph the first equation:



{{{x+y=3}}} Start with the first equation.



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



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



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Now let's graph the second equation:



{{{x+y=-1}}} Start with the second equation.



{{{y=-1-x}}} Subtract {{{x}}} from both sides.



{{{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 two equations together:



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



From the graph, we can see that the two lines are parallel, which means that they will <font size="4"><b>never</b></font> intersect. So there are no solutions. This means that the system of equations is inconsistent.