Point of Intersection of Linear Systems

Graphing

Graph the following equation:

$$y=-\frac{1}{2}x+2$$

Graphing

The black line represents $$y=-\frac{1}{2}x+2$$ .

Graph the following equation on the same grid.

$$3x+2y=8$$

**Remember, you need to convert it to slope-intercept form first.

Drag and Drop

The system of the linear equations below is graphed.

$$y=-\frac{1}{2}x+2$$

$$y=-\frac{3}{2}x+4$$

What is the intersection point of the system?



(​

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, ​

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)

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2

1

0

4

Open Ended

The system of the linear equations below is graphed.

$$y=-\frac{1}{2}x+2$$

$$y=-\frac{3}{2}x+4$$

This system is said to have 1 solution. What do you think that means?

Multiple Select

Which of the following graphed systems has one solution?

Select all that apply.

Dropdown

A system of equations with ​

Select answer

slopes have ​

Select answer

solution. These are ​

Select answer

lines.

Dropdown

The following goes in your notes:



A ​

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of linear equations is a ​

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with the ​

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.

Dropdown

The following goes in your notes:



A ​

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is an ​

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that is a ​

Select answer

to ​

Select answer

equations in the system.

Graphing

Graph the following linear equation:

$$y=\frac{3}{4}x+3$$

Graphing

The black line represents $$y=\frac{3}{4}x+3$$ .

Graph the following equation on the same grid.

$$3x-4y=16$$

**Remember, you need to convert it to slope-intercept form first.

Open Ended

The system of the linear equations below is graphed.

$$y=\frac{3}{4}x+3$$

$$y=\frac{3}{4}x-4$$

This system is said to have no solution. What do you think that means?

Multiple Choice

Which of the following graphs best represents a system of equations that has no solution?

Drag and Drop

A system of linear equations with the ​

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slope have ​

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solution. These lines are ​

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.

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same

no

negative

one

steep

parallel

perpendicular

intersecting

Graphing

The linear equation $$5x-2y=14$$ is graphed on the grid.

Graph another line to create a system of linear equations with infinitely many solutions.

Multiple Choice

Which of the following best describes a system of equations with infinitely many solutions.

Dropdown

A system of equations with the ​

Select answer

slope and the ​

Select answer

y-intercept has ​

Select answer

solutions. This is because it is the ​

Select answer

line.

Labelling

The following goes in your notes.

Click and drag to where each belongs.

Drag labels to their correct position on the image

One Solution

Same slope, same y-intercept

Different slopes

Infinitely Many Solutions

No Solution

Types of Solutions

Same slope, different y-intercepts

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The following goes in your notes.



Rewrite in ​

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form, if needed

Graph ​

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equation individually on the ​

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grid

Identify the Solution - the ​

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​

Check by​

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the x & y value of the solution into the original system

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slope-intercept

each

same

point of intersection

substituting

Graphing

The following goes in your notes

EX1: Graph $$y=-x+5$$

Be sure to graph in your notes CORRECTLY.

Graphing

The following goes in your notes

$$y=-x+5$$ is graphed in black.

EX1 Continued: Graph $$y=\frac{1}{3}x-3$$

Be sure to graph in your notes CORRECTLY.

Labelling

The following goes in your notes.

Graph the following system and find the solution.

$$y=-x+5$$

$$y=\frac{1}{3}x-3$$

Drag labels to their correct position on the image

(6, -1)

(-1, 6)

(-3, 0)

(0, 5)

(5, 0)

(-3, 5)

(5, -3)

(0, -3)

Graphing

The following goes in your notes.

EX2: $$y=3$$

Be sure to graph in your notes CORRECTLY.

Graphing

The following goes in your notes.

$$y=3$$ is graphed in black.

EX2 Continued: $$5x+4y=32$$

Be sure to convert to slope-intercept form FIRST.

Be sure to graph in your notes CORRECTLY.

Drag and Drop

The following goes in your notes.



Graph the following system and find the solution.



$$y=3$$

$$5x+4y=32$$



Solution:

(​

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, ​

Placeholder

)

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4

3

6

-5

8

Graphing

The following goes in your notes.

EX3: $$x+2y=4$$

Be sure to convert to slope-intercept form FIRST.

Be sure to graph in your notes CORRECTLY.

Graphing

The following goes in your notes.

$$x+2y=4$$ is graphed in black.

EX3 Continued: $$2y=-3x+4$$

Be sure to convert to slope-intercept form FIRST.

Be sure to graph in your notes CORRECTLY.

Drag and Drop

The following goes in your notes.



Graph the following system and find the solution.



$$x+2y=4$$

$$2y=-3x+4$$



Solution:

(​ ​

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, ​ ​

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)

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0

2

1

-1

Drag and Drop

The graphed line on the grid represents the first of two equations in a system of linear equations.



If the second equation passes through the points (-9, 2) and (-3, -4), what is the solution to the system?



(​

Placeholder

, ​

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)

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-7

0

4.5

-9

-4

-3

2

Open Ended

Things to remember

Multiple Choice

Which graph best represents this system of equations and its solution?

$$2x=6-y$$

$$5x-4y=28$$