Question 169128

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



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



{{{y=-3x+5}}} Rearrange the terms.



So we can see that the equation {{{y=-3x+5}}} has a slope {{{m=-3}}} and a y-intercept {{{b=5}}}.



{{{x+y=3}}} Now move onto the second equation.



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



{{{y=-x+3}}} Rearrange the terms.



So we can see that the equation {{{y=-x+3}}} has a slope {{{m=-1}}} and a y-intercept {{{b=3}}}.



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So the slope of the first line is {{{m=-3}}} and the slope of the second line is {{{m=-1}}}.



So the two slopes are NOT equal. This means that the two lines are NOT parallel.



Also, notice that if we multiply the slopes, we get {{{(-3)(-1)=3}}} which is NOT equal to -1. 
This means that the two slopes are NOT inverse reciprocals of one another. 

So the two lines are NOT perpendicular




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Answer:



So the two lines are neither parallel nor perpendicular.