Ch.+7+System+of+Equations

= Chapter 7 – Systems of Linear Equations =

• Use different strategies to solve a system of linear equations in two variables. • Use a linear system to model and solve a problem. • Find the number of solutions of a linear system. Systems of linear equations are used by: • Electricians, to find the current flowing through an electrical circuit and the voltage across the circuit • Economists, to assess supply and demand in an economy • Geneticists, to study the transmission of genes from one generation to another 1) **// System of linear equations / linear system //** – Two equations form a system of linear equation in two variables. A system of linear equations is often referred to as a linear system. A solution of a linear system is a pair of values that satisfy both equations. 2) **// Solve by substitution //** – we transform a system of two linear equations into a single equation in one variable, and use what we know about solving linear equations to determine the value of that variable. 3) **// Solve by elimination //** – adding or subtracting two equations in a linear system produces equivalent linear systems. We use this property to solve a linear system by first eliminating one variable by adding or subtracting the two equations. 4) **// Infinite Solutions //** – When two lines coincide, every point on one line is also a point on the other line; so all the points on the line are solutions. Thus there are infinite solutions (unlimited or without bound) 5) **// Equivalent systems //** – a system of equivalent equations that have the same solution as the original system. 7) **// Coincident lines //** – Lines with the same y-intercept and equal slopes.
 * What you’ll learn **
 * Why It’s Important **
 * Key Words **

Chapter 7 – Systems of Linear Equations Notes

 * ===[[file:1- 7.1a Developing Systems of Linear Equations key.pdf|1- 7.1a Developing Systems of Linear Equations I]] ===
 * ===[[file:2- 7.1b Developing Systems of Linear Equations II.pdf|2- 7.1b Developing Systems of Linear Equations II]] ===
 * ===[[file:3- 7.2 Solving a System of Linear Equations Graphically key.pdf|3- 7.2 Solving a System of Linear Equations Graphically ]] ===
 * ===[[file:4- 7.2 B - Solving a System of Linear Equations Graphically key.pdf|4- 7.2 Assignment - Solving a System of Linear Equations Graphically]] ===
 * ===[[file:5- 7.3 Using Graphing Technology to solve A system of linear Equations key.pdf|5- 7.3 Using Graphing Technology to solve A system of linear Equations]] ===
 * ===[[file:6- 7.4 Using Substitution As a Strategy to Solve Linear Systems key.pdf|6- 7.4 Using Substitution As a Strategy to Solve Linear Systems ]] ===
 * ===[[file:7- 7.5 Using Elimination to Solve a System of Linear Equations.pdf|7- 7.5 Using Elimination to Solve a System of Linear Equations]] ===
 * ===[[file:8- 7.6 Properties of Linear Equations.pdf|8- 7.6 Properties of Linear Equations]] ===
 * ===[[file:9- 7.7ApplicationsofSystemsWORKSHEET.pdf|9- 7.7ApplicationsofSystemsWORKSHEET]] ===
 * ===[[file:10- Ch. 7 Review key.pdf|10- Ch. 7 Review]] ===