Linear Systems
This unit continues the trend of systems- two or more things working together. A system of equations is a set of two or more equations that use the same variables. Linear equations, learned in Algebra 1 and reviewed in Unit 1, are graphed on the same coordinate plane as a linear system. It can be determined if there is one unique solution, infinite solutions, or no solution. Systems may be solved by graphing, substitution, or linear combinations. Each of these methods will be explored to determine their accuracy and when they are easiest to use. This discussion will include the definition of the standard form Ax+By=C of a linear equation. Systems of inequalities can also be graphed and solutions set shaded. With this background of the definition of systems and how to solve them, three variable systems are introduced. A third axis, the z-axis, changes mathematics from two-dimensional to three-dimensional. Graphs are no longer composed on coordinate plane but instead coordinate spaces. Solutions to these systems are called ordered triples. Systems can also be solved by inverse matrices and Cramer’s Rule. In linear algebra, matrices will be used to investigate and solve systems of linear equations in n variables. During this unit, problem solving using systems include real life situations such as mixture problems, distance problems, etc.
The bubble map above shows the different systems that we will be looking at in this unit.
Solving Absolute Value
DOWNLOAD PowerPoint on Solving Absolute Values.
DOWNLOAD Worksheet on Solving Absolute Value Equations.
DOWNLOAD Worksheet on Solving Absolute Value Inequalities.
Solving System of Inequalities by Graphing
DOWNLOAD PowerPoint on Solving System of Inequalities by graphing.
DOWNLOAD Worksheet on Solving System of Inequalities by graphing.
Solving 2x2 System of Equations
Linear Combination Method or Elimination Method (same thing)
DOWNLOAD PowerPoint on Solving 2x2 System of Equations using Linear Combination Method.
DOWNLOAD Worksheet on Solving 2x2 System of Equations using Linear Combination Method.
Solving 3x3 System of Equations
Linear Combination Method or Elimination Method (same thing)
DOWNLOAD PowerPoint on Solving 3x3 System of Equations using Linear Combination Method.
DOWNLOAD Worksheet on Solving 3x3 System of Equations using Linear Combination Method.
DOWNLOAD Worksheet on Solving 3x3 System of Equations using Substitution Method.
DOWNLOAD Worksheet on Solving 3x3 System of Equations using Cramer's Rule.
