GRAPHS OF SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES

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Mathematics

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8th Grade

•

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Rio Sioson

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14 Slides • 9 Questions

GRAPHS OF SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES

In this lesson you will be able to categorize when a given system of linear equations in two variables has a graphs that are parallel, intersecting, and coinciding.

Multiple Choice

Describe the graph:

parallel

coinciding

intersecting

Multiple Choice

Describe the graph:

parallel

conciding

intersecting

Multiple Choice

Describe the graph:

parallel

coinciding

intersecting

Show the graph of each pair of linear equations below.

3x+y=2 and 2x-y=3
3x-y=4 and y=3x+2
x+3y=6 and 2x+6y=12

A SYSTEM OF LINEAR EQUATIONS

A solution of such equations is an ordered pair of numbers that satisfies both equations.

The solution set of a system of linear equations in two variables is the set of all ordered pairs of real numbers that makes every equation in the system true.

A SYSTEM OF LINEAR EQUATIONS HAS:

a. only one solution if their graphs intersect at only one point.

System of CONSISTENT and INDEPENDENT equations

This is a system of linear equations having exactly one solution. The slopes of the lines defined by the equations are not equal; their y-intercepts could be equal or unequal; and their graphs intersect.

A SYSTEM OF LINEAR EQUATIONS HAS:

b. no solution if their graphs do not intersect.

System of INCONSISTENT equations

This is a system of linear equations having no solution. The slopes of the lines defined by the equations are equal, their y-intercepts are not equal; and their graphs are parallel.

A SYSTEM OF LINEAR EQUATIONS HAS:

c. infinitely many solutions if their graphs coincide.

System of CONSISTENT and DEPENDENT equations

This is a system of linear equations having infinitely many solutions. The slopes of the lines defined by the equations are equal, their y-intercepts are also equal, and their graphs coincide.

Multiple Choice

Determine whether each system of linear equations in two variables has graphs that are parallel, intersecting, and coinciding.

parallel

intersecting

coinciding

Multiple Choice

parallel

intersecting

coinciding

Multiple Choice

parallel

intersecting

coinciding

Fill in the Blanks

If the slopes of two lines are equal; their y-intercepts are also equal, then their graphs are

Type answer...

Fill in the Blanks

If the slopes of two lines are not equal; their y-intercepts could be equal or unequal; and their graphs are

Type answer...

Poll

OVERALL ASSESSMENT OF THE LESSON

EXCELLENT

VERY SATISFACTORY

GOOD

POOR

THANK YOU!

GRAPHS OF SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES

In this lesson you will be able to categorize when a given system of linear equations in two variables has a graphs that are parallel, intersecting, and coinciding.

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