Question

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

Answer 1

One

Answer 2

ONLY ONE PAIR OF SOLUTION EXISTS
@gabbie96

Answer 3

Hmmmmm..... nope, look again.

Notice anything "fishy" about those two equations?

Answer 4

Ohhh, I read it wrong! They're the same equation, aren't they?

Answer 5

@gabbie96 , what do you notice?

Answer 6

you can re-arrange the first equation:
x + y = 1
y = 1 - x

so we then have
y = 1 - x
y = -x + 1

it's the same equation.

Answer 7

One way to see what "kind" of system you have, is to solve both equations for y.

If you get the SAME equation, then the system is dependent: it's just one line, so EVERY point on that line is a solution, so infinite solutions.

Answer 8

If you get two lines with the same slope (but different y-intercepts) then they are parallel lines, so NO solutions, since they never intercept.

Answer 9

Wouldn't this mean there are an infinite number of solutions? As long as x and y add up to 1 then it works.
example:
x=-2, y=3
x=1, y=0
I don't know, I could be wrong.

Answer 10

and if you get two distinct, non-parallel lines (all other cases) then you get one solutions, since there is one point of interception.