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)