# WEEK 21-SYSTEMS-OF-LINEAR-EQUATIONS

VIMSCHOOL

Created on September 20, 2024

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## Transcript

Objectives

Start

Systems of Linear Equations

1

2

Story

System of Equations

Summary

Graphical Method

Story

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1

In the following video, pay close attention to the mentioned problem.

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System of Equations

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What is a system of two equations with two unknowns? or 2x2 system

Definition: A 2x2 system of linear equations is in the form:

Here:

are the unknown variables

are the coefficients

x and y

a, b, c, d, e,

Example 1: The following is a linear system:

ax+by=c₁dx+ey=c₂

y-2x=34y+2x=1

are the constants

c₁, c₂

x and y are the unknown variables. 1,-2, 4, 2 are the coefficients. 3 and 1 are the constant terms.

Finding Possible Solutions of 2x2 systems

Example 1: Find solutions of the system:

x=2, y=4

x+y=6x+2y=10

🗨️

In order to solve a linear system of two variables, try with values that satisfy both equations.

1

x=0, y=6x=1, y=5x=2, y=4x=3, y=3

and their counterparts (like x=6, y=0)

For x=2, y=4:

2+4=62+2(4)=10

1. Think of it as follows: The sum of two numbers is 6 and the 1st number + twice the the 2nd number is 10 What are the numbers?

2. Think of a list of possible numbers which satisfy the 1st equation.

3. Replace values into the equation until you get the values that satisfy the right hand side.

Too abstract?! Think of it as follows: The sum of two numbers is 6 and the 1st number + twice the the 2nd number is 10 What are the numbers?

Try it by yourself:

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Graphical Method

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1

In the graphical method, we plot each of the equations in a Cartesian Plane.

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Let's see some examples:

Find the solution of the system:

x=-1y=2

Step 3

Step 2

Step 1

Step 4

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Create a table of values for the first line and plot the line in a Cartesian plane. y=-x+1 xy0110

Create a table of values for the 2nd equation and plot on the same plane as 1st line. y=x+3 xy0314

Estimate the intersection between the two lines by finding the coordinates on the Cartesian plane.

Verify the solution encountered: y = x + 3 2 = (-1) + 3 2 = 2 ✔ y = -x + 1 2 = -(-1) + 1 2 = 2 ✔

Try it by Yourself

Solve the system of equations:

Click here to draw >

Solution

x+y=1x-y=1

Equation 1

Equation 2

x=0y=1

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Data follows a positive association.

1. Solve each equation for y

2. Create a table of values for both equations.

3. Plot points of both equations and join them on the Cartesian plane.

4. Find the intersection between two lines.

Verify the solution encountered:

Summary: Solving Systems of Equations by Graphing

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

8TH-SYSTEMS-OF-LINEAR-EQUATIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

It is highly advised to have:

MATERIAL

- 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 multipleways."