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Chapter 8: Systems of Equations
Transcript of Chapter 8: Systems of Equations
& Hayden Gibson What is a System of Equations? A system of equations is when you have two or more equations using the same variables. The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair. When graphing, you will encounter three possibilities _ Intersecting Lines: The point where the lines intersect is your solution.
_ Parallel Lines: These lines never intersect! Since the lines never cross, there is NO SOLUTION! Parallel lines have the same slope with different y-intercepts.
_ Coinciding Lines: These lines are the same! Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! Coinciding lines have the same slope and y-intercepts. When graphing equations, graph using the x- &y- intercepts (plug in zeros)
ex: 2x + y = 4
x - y = 2
2x + y = 4 x - y = 2
(0,4) and (2,0) (0,-2) and (2,0)
then graph the ordered pairs.
Where do the lines intersect? They intersect at (2,0)! Be sure to check your answers!
Plug the point back into both equations. . .
does it work? yes! How to tell if a line is "intersecting", "parallel", or "coinsiding": The system has exactly 1 solution.
Systems have 1 and only 1 solution when the two lines have different slope. Think about it, if the two lines have different slopes then eventually at some point they must meet. After all the lines are not parallel.