Linear Systems Graph

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 ​

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slopes have ​

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solution. These are ​

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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

Same slope, different y-intercepts

Infinitely Many Solutions

One Solution

Different slopes

Types of Solutions

Same slope, same y-intercept

No Solution

Drag and Drop

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

(-3, 5)

(5, 0)

(6, -1)

(-3, 0)

(0, 5)

(5, -3)

(0, -3)

(-1, 6)

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:

(​

Placeholder

, ​

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

, ​

Placeholder

)

Drag these tiles and drop them in the correct blank above

-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?

$$2x=6-y$$

$$5x-4y=28$$