Systems of Linear Equations
Objectives
Start
Story
System of Equations
Graphical Method
Summary
Story
In the following video, pay close attention to the mentioned problem.
🗨️
System of Equations
What is a system of two equations with two unknowns? or 2x2 system
Definition: A 2x2 system of linear equations is in the form:
ax+by=c₁dx+ey=c₂
Example 1:
The following is a linear system:
x and y
are the unknown variables
c₁, c₂
Here:
y-2x=34y+2x=1
are the constants
a, b, c, d, e,
are the coefficients
Finding Possible Solutions of 2x2 systems
In order to solve a linear system of two variables, try with values that satisfy both equations.
🗨️
Example 1:
Find solutions of the system:
x=0, y=6x=1, y=5 x=2, y=4 x=3, y=3
and their counterparts (like x=6, y=0)
x+y=6x+2y=10
For x=2, y=4:
2+4=62+2(4)=10
x=2, y=4
Try it by yourself:
Graphical Method
In the graphical method, we plot each of the equations in a Cartesian Plane.
🗨️
Let's see some examples:
Find the solution of the system:
x=-1y=2
Step 4
Step 3
Step 1
Step 2
Click here to draw >
Try it by Yourself
x=0y=1
x+y=1x-y=1
Solve the system of equations:
Equation 1
Equation 2
Solution
Summary:
Solving Systems of Equations by Graphing
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
8TH-SYSTEMS-OF-LINEAR-EQUATIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- A compass.
- A Protactor.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).
MA.8.AR.4 Develop an understanding of two-variable systems of equations. MA.8.AR.4.1 Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations. MA.8.AR.4.3 Given a mathematical or real-world context, solve systems of two linear equations by graphing. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. MA.K12.MTR.6.1 Assess the reasonableness of solutions. MA.K12.MTR.2.1 "Demonstrate understanding by representing problems in multiple ways."
WEEK 21-SYSTEMS-OF-LINEAR-EQUATIONS
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Created on September 20, 2024
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Transcript
Systems of Linear Equations
Objectives
Start
Story
System of Equations
Graphical Method
Summary
Story
In the following video, pay close attention to the mentioned problem.
🗨️
System of Equations
What is a system of two equations with two unknowns? or 2x2 system
Definition: A 2x2 system of linear equations is in the form:
ax+by=c₁dx+ey=c₂
Example 1: The following is a linear system:
x and y
are the unknown variables
c₁, c₂
Here:
y-2x=34y+2x=1
are the constants
a, b, c, d, e,
are the coefficients
Finding Possible Solutions of 2x2 systems
In order to solve a linear system of two variables, try with values that satisfy both equations.
🗨️
Example 1: Find solutions of the system:
x=0, y=6x=1, y=5 x=2, y=4 x=3, y=3
and their counterparts (like x=6, y=0)
x+y=6x+2y=10
For x=2, y=4:
2+4=62+2(4)=10
x=2, y=4
Try it by yourself:
Graphical Method
In the graphical method, we plot each of the equations in a Cartesian Plane.
🗨️
Let's see some examples:
Find the solution of the system:
x=-1y=2
Step 4
Step 3
Step 1
Step 2
Click here to draw >
Try it by Yourself
x=0y=1
x+y=1x-y=1
Solve the system of equations:
Equation 1
Equation 2
Solution
Summary: Solving Systems of Equations by Graphing
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
8TH-SYSTEMS-OF-LINEAR-EQUATIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
MA.8.AR.4 Develop an understanding of two-variable systems of equations. MA.8.AR.4.1 Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations. MA.8.AR.4.3 Given a mathematical or real-world context, solve systems of two linear equations by graphing. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. MA.K12.MTR.6.1 Assess the reasonableness of solutions. MA.K12.MTR.2.1 "Demonstrate understanding by representing problems in multiple ways."