A system of linear equations has a graph of 2 intersecting lines.

Part 1: Are the slopes the same or different?

Part 2: Are the x and y intercepts the same or different?

Part 3: How many solutions would this system of equations have?

Question

A system of linear equations has a graph of 2 intersecting lines.

Part 1: Are the slopes the same or different?

Part 2: Are the x and y intercepts the same or different?

Part 3: How many solutions would this system of equations have?

campbell_st · Answer

the lines need different slopes to intersect. If the slopes are the same they are parallel. 

for the lines to intersect they intercepts are different. The lines can have 1 intercept the same...i.e. same x or same y... which means that is the point if intersection. 

if both the intercepts are the same, the lines are the same... 

well if the lines are have different slopes there is 1 solution. 

same slopes no solutions 

same intercepts infinite solutions.