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MPM 2DIUnit 1: Solving Linear Systems
Day 1: Solving Linear Systems by Graphing
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.
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)
b) Use the Intercept Method
∴ The solution is (0, 3)
c) Use the Slope - y-Intercept Method
∴ The solution is (0, -4)
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.
Practice: p. 61 #5 - 9 (parts a and c for each)