Graph the following linear system to determine the number of solutions.
y=-x+2
x+y=5

0
1
2
infinitely many

Question

Graph the following linear system to determine the number of solutions.
y=-x+2
x+y=5

0
1
2
infinitely many

anonymous · Answer

replace the y in x+y with -x + 2

mathmate · Answer

Rewrite the equations:
$$y=-x+2$$
$$y=-x+5$$
Do you notice anything?

anonymous · Answer

it would equal 2=5 right?

anonymous · Answer

so 0 solutions?

mathmate · Answer

Since $2\ne 5$, what does that tell you about the system?

anonymous · Answer

it can't have an solution, right?

mathmate · Answer

exactly!

mathmate · Answer

Graphically it means:
|dw:1404589490665:dw|
and the two lines will never meet (parallel), so there's no solution.

texaschic101 · Answer

true....when the equations have the same slope, but different y-intercepts, that means the lines are parallel, thus, having no solution.

Now if the equations would have had the same slope and the same y intercept, then the answer would have been infinite solutions.
And if the equations would have had different slopes and different y intercepts, then they would have 1 solution.