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# Systems of Linear Equations Introduction

I. General Form:
a1 x + b1 y = c1
a2x + b2y = c2
where ai, bi, and ci are constants

II. Methods for Solving:
a. Graphing
b. Substitution
c. Addition (a.k.a., the “elimination method”)
d. Matrices
1. row-reduction (section 3.4, not covered)
2. determinants (section 3.5, not covered)
3. matrix inverse (not in text, not covered)

I. A Graphing Example (p.174): Exercise #10

II. Two Lines, Three Possibilities
1. Lines intersect at a point, whose (x,y)-
coordinates are the “unique” ordered pair
solution...
2. Lines are parallel (never intersect), no
ordered pair satisfying both equations
exists, and thus there is no solution...
3. Lines are the same and all the points on it
have (x,y)-coordinates which satisfy both
equations, and thus there are an infinite
number of solutions...

III. A Substitution Example (p.175): Exercise #32

IV. An Elimination Example (p.175): Exercise #48

V. Practice Problem (p.175): Exercise #64,40

HW: pp.174-175 / Exercises #3-79 (every other odd)