Determine if the system y=2x+5 , y=-x+2 has a solution by graphing each line. Make sure to show the x and y-intercepts of each line and your calculations. If there is a solution, you do not have to determine it; only say why there is, or is not a solution based on the graphs. Please help!

Question

anonymous · Answer

http://www.wolframalpha.com/input/?i=y%3D2x%2B5+%2C+y%3D-x%2B2&dataset=

anonymous · Answer

@shubham.bagrecha So it is a solution?

anonymous · Answer

yes

anonymous · Answer

But how do they get -1 and 3? @shubham.bagrecha

anonymous · Answer

'coz the lines are meeting at (-1,3)

anonymous · Answer

To satisfy the system, the solution must be a solution to both lines, and avery point on a line  satisfy its equation, but the point that satisfy both needs to be on both lines, that is why the fact that they meet says that there is a solution. Also, to know if they meet without graphing it, you need to look at the slope, they only intersect if they are not paralel, and the only way they are paralel is when the slopes are equal, and on the given equations they are not, so it has a solution.

anonymous · Answer

Thank you @shubham.bagrecha and @ivanmlerner