MATH 0322 Intermediate Algebra Unit 4 Review Slope
MATH 0322 Intermediate Algebra Unit 4 Review: Slope and Slope-Intercept
Slope and Slope-Intercept Form • slope
Slope and Slope-Intercept Form • increases decreases constant
Slope and Slope-Intercept Form •
MATH 0322 Intermediate Algebra Unit 4 Section 3. 5 Point-Slope Equation
Point-Slope Form •
Point-Slope Form • Standard Form Vertical Line Form Horizontal Line Form Slope-Intercept Form Point-Slope Form
Point-Slope Form •
Point-Slope Form • P P P
Point-Slope Form • P P
Point-Slope Form • P P
Point-Slope Form • P P
Point-Slope Form • P P
Point-Slope Form • P P
Point-Slope Form • P
Point-Slope Form • P
Complete and Practice HW 3. 5
MATH 0322 Intermediate Algebra Unit 4 Solving Systems of Linear Equations (Graphing Method) Section: 4. 1
Solving Systems of Linear Equations (Graphing Method) • Intersect once Eqt#2 Intersect many times Eqt#1 One solution Eqt#1 Eqt#2 Infinitely many solutions Never intersect Eqt#2 Eqt#1 No solution
Solving Systems of Linear Equations (Graphing Method) • Equation #1 or Equation #2 goes here.
• Solving Systems of Linear Equations (Graphing Method) P O Not a solution. P
• Solving Systems of Linear Equations (Graphing Method) Yes P P P
• Solving Systems of Linear Equations (Graphing Method) ? ? P P
• Solving Systems of Linear Equations (Graphing Method) Parallel lines P
Solving Systems of Linear Equations (Graphing Method) q Without graphing, how can you tell if a Linear System in Slope-Intercept form has: ? One solution ? Infinitely many solutions ? No solution
• Solving Systems of Linear Equations (Graphing Method) P
Graphing Method Complete and Practice HW 4. 1
MATH 0322 Intermediate Algebra Unit 4 Solving Systems of Linear Equations (Substitution Method) Section: 4. 2
Solving Systems of Linear Equations (Substitution Method) Ø This section introduces the Substitution Method: an algebraic method that substitutes the value of a variable from one equation into the other equation to solve a Linear System. Ø To solve a Linear System using this method: 1) Isolate a variable. (simplest one) 2) Substitute into other equation, solve 1 st solution. 3) Back-substitute into an original equation, solve 2 nd solution, then Check.
Solving Systems of Linear Equations (Substitution Method) Ø 3 types of results: One solution Infinitely many solutions Graphing Method Substitution Method No solution
• Solving Systems of Linear Equations (Substitution Method) P P
• Solving Systems of Linear Equations (Substitution Method) P P
• Solving Systems of Linear Equations (Substitution Method) P
• Solving Systems of Linear Equations (Substitution Method) ?
• Solving Systems of Linear Equations (Substitution Method) ? ?
• Solving Systems of Linear Equations (Substitution Method)
• Solving Systems of Linear Equations (Substitution Method) ?
Solving Systems of Linear Equations (Substitution Method) • P
• Solving Systems of Linear Equations (Substitution Method) P System has no solution.
Substitution Method Complete and Practice HW 4. 2
MATH 0322 Intermediate Algebra Unit 4 Solving Systems of Linear Equations (Addition Method) Section: 4. 3
Solving Systems of Linear Equations (Addition Method) •
Solving Systems of Linear Equations (Addition Method) •
Solving Systems of Linear Equations (Addition Method) Ø 3 types of results: One solution Infinitely many solutions Graphing Method Substitution Method Addition Method No solution
• Solving Systems of Linear Equations (Addition Method) Yes P P P
Solving Systems of Linear Equations (Addition Method) • No P P Equation #1
• Solving Systems of Linear Equations (Addition Method) Step 1) Step 2) Step 3) P
• Solving Systems of Linear Equations (Addition Method) Step 1) Infinitely many solutions P
Solving Systems of Linear Equations (Addition Method) • Step 1) Yes Step 2) Step 3) P P
Addition Method Complete and Practice HW 4. 3
MATH 0322 Intermediate Algebra Unit 4 Appendix B: Matrices
Matrices • System of Equations Matrix
Matrices •
Matrices • Row-Echelon form: Ø If last row looks like this, o System has One Solution. o System is Consistent. o Equations are Independent. Ø If last row looks like this, o System has Infinitely Many Solutions. o System is Consistent. o Equations are Dependent. Ø If last row looks like this, o System has No Solution. o System is Inconsistent.
Matrices • P P
Matrices •
Matrices • To solve a System of Equations using matrices: 1) Write augmented matrix. 2) Apply Row Operations to get Row-Echelon form. 3) Rewrite rows as equations, then Back-Substitute to determine solution set.
Matrices • P P
Matrices • P
Matrices • P
Matrices • P
Matrices •
Matrices •
Matrices •
Matrices • P
• Matrices 2) Apply Row Operations to get Row-Echelon form.
Appendix B: Matrices Complete and Practice
Point-Slope Form •
- Slides: 73