3.1 1

Section 3.1Introduction to Systems of Equations Any pair of Linear Equations can be a System

A Solution Point must make both equations true When plotted on the same graph, the solution is

the point where the lines cross (intersection) Some systems do not have a solution

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System of Two Equations

1264

622

yx

yx

B

A

Solution point (3,0)

Please Note: I use A and B notation, different from the (1) (2) used in your text

3.1 3

Why Study Systems of Equations?

We will first study systems of 2 equations in 2 unknowns (usually x and y)

The methods we use to solve them will also be useful in higher degree systems that involve quadratic equations or systems of 3 equations in 3 unknowns

3.1 4

Find the Equations: Put Data into Tables or Formulas

____(p)ostcard stamps and ____ (f)irst-class stamps were bought

33903723

120

fp

fp

B

A

Guessing … How about 100 first class stamps?

Guessing … How about 70 first class stamps and 50 postcard stamps?

37(70)= 2590 23(50)= 1150 sum is 3740 ! Oops, we need a better way

37(100)=$37.00 Oops, way too much!

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Find the Equations: Separate Data from Noise

Americans bought ____ gal (w)ater and ____ gal of (s)oft drinks

3.1 6

Checking a Proposed Solution

B

A

3.1 7

Approximation …Solving Systems Graphically

B

A

3.1 8

Practice – Solving by GraphingConsistent: (1,2) Inconsistent: no solutions Consistent: infinite sol’s

3.1 9

Find the Intersection: Put Data into Tables or Formulas

____(p)ostcard stamps and ____ (f)irst-class stamps were bought

33903723

120

fp

fp

3.1 10

And furthermore …

Section 3.2 Solving by Substitution or Elimination