Algebra Tutorials!
 
 
   
Home
Rational Expressions
Graphs of Rational Functions
Solve Two-Step Equations
Multiply, Dividing; Exponents; Square Roots; and Solving Equations
LinearEquations
Solving a Quadratic Equation
Systems of Linear Equations Introduction
Equations and Inequalities
Solving 2nd Degree Equations
Review Solving Quadratic Equations
System of Equations
Solving Equations & Inequalities
Linear Equations Functions Zeros, and Applications
Rational Expressions and Functions
Linear equations in two variables
Lesson Plan for Comparing and Ordering Rational Numbers
LinearEquations
Solving Equations
Radicals and Rational Exponents
Solving Linear Equations
Systems of Linear Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
DISTANCE,CIRCLES,AND QUADRATIC EQUATIONS
Solving Quadratic Equations
Quadratic and Rational Inequalit
Applications of Systems of Linear Equations in Two Variables
Systems of Linear Equations
Test Description for RATIONAL EX
Exponential and Logarithmic Equations
Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
Literal Equations & Formula
Equations and Inequalities with Absolute Value
Rational Expressions
SOLVING LINEAR AND QUADRATIC EQUATIONS
Steepest Descent for Solving Linear Equations
The Quadratic Equation
Linear equations in two variables
   
Try the Free Math Solver or Scroll down to Resources!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


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)
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

  Copyrights © 2005-2024