1.Which pair of equations has graphs that are intersecting? How many points intersection do the graphs have? 2.Which pair of equations has graphs that are not intersecting? How do you describe these equations? 3.How would you compare slopes of the lines in each system? How about their y-intercepts? 4.What is your observation about the solution of the system in a relation to the slopes and y-intercepts?
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1) A system of linear equations has one solution when the graphs intersect at a point.
2) There will be a maximum 6 intersection points between 4 lines. Between 2 circles there are 2 intersection points. Between one line and one circle, there are maximum 2 intersection points.
3) If the two lines have different slopes, the system has exactly one solution (whether the lines have the same intercept or different intercepts).
If they have the same slope and the same intercept they are the same line, so there are infinitely many solutions to the system.
If they have the same slope and different intercepts then they are parallel and there is no solution to the system.
4) The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.
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