MPM 2DIUnit 1: Solving Linear Systems

Day 2: Solving Linear Systems by Graphing and How Lines Intersect

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.

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

Practice: p. 61 #5 - 9 (part a for each)

pg. 69 #1 – 5, 12