WEEK-21-SOLUTION-OF-ARBITRARY-SYSTEMS-OF-EQUATIONS

Solution of Arbitrary Systems of Equations

Objectives

Start

Definition and Solutions

Graphical Method

Substitution Method

Elimination Method

Summary

Definition and Solutions

What is a system of equations?

Definition

Linear Equations

Polynomial Equations

Graphical Method

System of equations of two variables can be solved by graphing the two equations.

x=-1y=2

Find the solution of the system:

Try It By Yourself

Substitution Method

Method of Solution

Example

Find the solution of the system:

x=-1y=1

Step 4

Step 3

Step 1

Step 2

Elimination Method

Method of Solution

Example

Find the solution of the system:

x=3y=-1

Step 4

Step 3

Step 1

Step 2

(4)

(3)

Choose the correct answer

Summary

Great job!

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Solve for one variable

in one of the equations.

eliminate a variable

by adding or subtracting the equations.

Replace value on the former equation

and solve for the other variable

MA.912.AR.9 Write and solve a system of two- and three- variable equations and inequalities that describe quantities or relationships. MA.912.AR.9.2 Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically. MA.912.AR.9.3 Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically. MA.912.AR.9.9 Given a mathematical or real-world context, solve a system of three-variable linear equations algebraically. MA.K12.MTR.7.1 Apply mathematics to real-world contexts.

Check the Solution

Whether the solution makes sense or no.

Eliminate the other variable

or use substitution method to find the other variable.

If there are more variables left

Replace the value obtained into the oher equation to solve the variable left.

Replace on the other equation

and solve for the remaining variable

Solve for one variable

in one of the equations.

If there are more variables left,

eliminate the other variable from other pair of equations.

Check the Solution

Whether the solution makes sense or no.