How many solutions exist for the system, x + y = 1 and y = -x + 1?

infinitely many solutions

no solution

one solution

Question

How many solutions exist for the system, x + y = 1 and y = -x + 1?

	
infinitely many solutions
	
no solution
	
one solution

xapproachesinfinity · Answer

x+y=1 and y=-x+1
those are the same equation

xapproachesinfinity · Answer

how many points that lie on that line satisfying x+y=1

xapproachesinfinity · Answer

what do you think?

xapproachesinfinity · Answer

how many points would satisfy x+y=1
just use some logic!!

anonymous · Answer

one solution

xapproachesinfinity · Answer

no!
there are so many points that give us x+y=1

anonymous · Answer

infinitely many solutions then

xapproachesinfinity · Answer

one solution is when we have two distinct line
intersecting on one points
that point is the solution to the system determined by the equations of those two line

xapproachesinfinity · Answer

yes!

xapproachesinfinity · Answer

but i don't think you got this yet

xapproachesinfinity · Answer

what if two lines  are parallel to each other
how many solutions will there be?

anonymous · Answer

many

xapproachesinfinity · Answer

hmm...
first you need to know that there is a solution only when there is intersection
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many solution only in one case where two lines coincide (meaning the same line )

xapproachesinfinity · Answer

so when two line are parallel
there is no solution