Solving Linear Systems by Graphing 3.1

1
Solving Linear Systems by Graphing 3.1

• Does solving linear systems by graphing always
  produce an accurate solution?
• What is the best use for solving linear systems
  by graphing?

2
What is a linear system?

• A linear system is two linear equations in two
  variables x and y in the form of

A solution of a system of linear equations in two
variables is an ordered pair (x,y) that satisfies
each equation.
3
Check whether (a) (2,2) and (b) (0,-1) are
solutions of the following systems.

• (a) 3(2) -2(2) 2
• 2 2(2) 6
• Since (2,2) is a solution of each equation, it is
  a solution, it is a solution of the system.
• 3(0) -2(-1) 2
• 0 2(-1) -2?6
• Since (0,-1) is not a solution of the 2nd
  equation, it is not a solution of the system.

4
Solve the system by graphing.

• (2,1)

5
Tell how many solution the linear system has.

• Infinitely many solutions

6
Tell how many solution the linear system has.


No solution
7
One solution

• GraphingThe graph of the system is a pair of
  lines that intersect in one point.
• AlgebraThe system has exactly one solution.

8
Infinitely Many Solutions
GraphingThe graph of the system is a single
line AlgebraThe system has infinitely many
solutions.
9
Number of solutions of a Linear System
GraphingThe graph of the system is a pair of
parallel lines so that there is no point of
intersection. AlgebraThe system has no solution.
10
Assignment 3.1

• Page 142, 12-30 every 3rd problem, 32-40 all, 42,
  51