SOLUTION: how do I find out with a graph that already has the points plotted if it has no solutions, one, or many?

Question 1063259: how do I find out with a graph that already has the points plotted if it has no solutions, one, or many?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let's say you have four points A,B,C,D plotted on the same xy grid. Let's further say that you know A and B lie on the same line. So that means we can draw a line through A and B. Call this line m.

If C and D are on the other line, then draw a line through those two points. Call this line n.

There are 3 different possible scenarios

Scenario 1: Line m and line n cross at exactly 1 point. This is the point of intersection and it is the solution to the system. This system has 1 solution.

Scenario 2: The two lines are parallel. This can be visually confirmed or you can determine the slope of each line. The two lines would have equal slopes but different y intercepts if they are parallel. There are no solutions (since the lines never cross)

Scenario 3: The two lines are actually one in the same. One line is perfectly right on top of the other line. This means there are infinitely many solutions.

RELATED QUESTIONS
Graph the system below and write its solution. {4x+2y=6 {y=-2x+3 *It's either no... (answered by Fombitz)

Graph the system below and write its solution. {4x+2y=6 {y=-2x+3 *It's either no... (answered by Fombitz)

Graph the linear system and determine how many solutions it has: no solution, exactly one (answered by rothauserc)

james and max are saving up their allowances to buy laptop computers. James has to saved... (answered by stanbon)

Find the slope of (5,0) (-6,-4) These are the points that I have already plotted onto... (answered by solver91311,jim_thompson5910)

Graph each system of equations. Determine whether the system has no solutions, one... (answered by Alan3354)

Okay so I have two points and a shaded graph with nothing to plug the points into and I... (answered by sofiyac)

please I need help with this one question I need to graph this problem 3x-y=-9 and... (answered by solver91311)

3x-y=-3 2x+y=-7 i am trying to figure out how to find the x,y,xy corrdinates so i can (answered by jim_thompson5910,vleith)