mpm 2di unit 1: solving linear...
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MPM 2DIUnit 1: Solving Linear Systems
Day 2: Solving Linear Systems by Graphing and How Lines Intersect
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What is a Linear System?
● A linear system is a set of two linear equations
● A linear system can be solved either graphically or algebraically
● A solution to a linear system is a coordinate point that satisfies BOTH equations. Graphically, it is the point of intersection of the lines.
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Example: Solve each of the following systems using the method of graphing indicated.
a) Use a Table of Values
x y
-2
-1
0
1
2
x y
-2
-1
0
1
2
-5
3
1
-1
-3
-9
3
0
-3
-6
∴ The solution is (2, 3)
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b) Use the Intercept Method
∴ The solution is (0, 3)
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c) Use the Slope - y-Intercept Method
∴ The solution is (0, -4)
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How do you know which graphing method to use?Table of Values● When all the equations are relatively easy to solve (i.e. no fractions
and small values)● If you don’t know what the graph will look like (linear?)Slope - y-Intercept Method● When the equation is given in y = mx + b form● The slope and y-intercept are relatively easy to graph (i.e. a y-intercept of 200 and a with a slope of 2 may be difficult to graph with this method)
The Intercept Method● When the equation is in the form Ax + By = C ● When the equation is in the form y = mx + b but the slope and y-intercept are not easy to graph.
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How can lines intersect?In a linear system with no solutions, the two linear equations have the ________ slope and _____________ y-intercepts. The lines are ____________________________.
In a linear system with one solution, the two linear equations have ______________ slopes. The y-intercepts have __________ influence.
In a linear system with infinite (many) solutions, the two linear equations have the ______________ slope and the _______________ y-intercept. They are ______________________________ lines.You can determine how many solutions a system of equations has just by looking at their equations and comparing their ______________ and _______________________.
same
samesame
differentparallel
differentno
co-incident (identical)
slopes y-intercepts
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Practice: p. 61 #5 - 9 (part a for each)
pg. 69 #1 – 5, 12