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Systems of Linear Equations
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Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
Literal Equations & Formula
Equations and Inequalities with Absolute Value
Rational Expressions
Steepest Descent for Solving Linear Equations
The Quadratic Equation
Linear equations in two variables
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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
  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)
Read section 3.2 (pp.178-189)

I. Word Problem Guidelines #2: see website link

II. Examples (p.190): Exercises #10,16

HW: pp.189-190 / Exercises #1,3,9,11,13,17

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