Systems of Equations Graphing Review

Multiple Choice

Which of the following is not a method to solve systems?

• Elimination
• Difference of Squares
• Substitution
• Graphing

Graphing to solve a system of equations.

Vocabulary

Intersecting Lines: Lines that meet or cross at one point are said to intersect​ and have One Solution. Intersecting lines have different slopes.

​

​Parallel Lines: Lines that have the same slope and different y-intercept, parallel lines have No Solution​ to the system of equations

Same Line: Lines that have the same slope and the same y-intercept are said to be the same. The Solution to a system with the same lines is said to have an Infinite number of Solutions​

Multiple Select

What is a solution to a graphed system of linear equations? (select all correct options)

• The point where both lines intersect

• The point where the y-axis and x-axis meet

• An ordered pair that both lines share

• A salt dissolved in water

Multiple Choice

When would we get "infinitely many solutions" to a system of equations?

• The lines are parallel, never intersecting

• The lines cross at one point

• The lines are the same and overlap at all points

• The lines cross at 2 points

Multiple Choice

When will we get "no solutions" from a system of equations?

• The two lines cross once

• The two lines are the same and overlap

• The two lines are parallel and never touch

• The two lines cross at 2 points

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Multiple Choice

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Multiple Choice

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

Graphing

Place a point at the solution to the system of equations graphed.

Solve by graphing

​Make sure equations are in y = mx + b form.

1. Graph the first line using the y-intercept and slope.

2. Graph the second line using the y-intercept and slope.

3. Look for the point where the two lines intersect.

4. Make sure that your solution is written as (x, y)

5. Identify no solution or infinite solutions situations.

Multiple Choice

What form do we need the equations to be in so that we can graph them?

• Standard From

• Slope-Intercept Form

• Point-Slope Form

• Any Form

Multiple Choice

What would the solution be to this system of linear equations? (click on the picture for a closer look).

• (0,-1.5)

• (1, -3)

• (5,0)

• (0,0)

Multiple Choice

What would the solution be to this system of linear equations? (click on the picture for a closer look.)

• (0,0)

• (2,2)

• (6,0)

• (0,4)

Multiple Choice

These two lines intersect at _____. (click to enhance)

• (4, -2)

• (4, 2)

• (-2, 4)

• No solution

Multiple Choice

Based on the graph of the following system, determine the solution.

• $$\left(4,2\right)$$

• $$\left(1,4\right)$$

• $$\left(2,4\right)$$

• no solution

Multiple Choice

What is the solution to this system?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Graphing

Graph the equation:

y = 3x + 2

Graphing

Graph the equation by creating 3 points on the graph:

1. Place a point on the y-intercept

2. Use slope to place the next point on the line.

3. Use slope in reverse to place a point to the left of the y-intercept.

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

Graphing

Graph the equation:

y = 2

Draw

Graph the system using the drawing tool. The next question will ask for the solution. Red: y = x + 3 & Blue: y = -2x

Drag and Drop

The solution to: y = x + 3 and y = -2x is (​

Placeholder

,​

Placeholder

).

Drag these tiles and drop them in the correct blank above

-1

2

3

1

-3

-2

0

Draw

Use the drawing tool to graph the lines. The next slide will ask for the solution. Red: y = -3x + 5 & Blue: y = -x - 1.

Fill in the Blanks

What is the solution to the system from the previous slide: y = -3x + 5 and y = -x - 1?

​​If you don't understand then you can watch this video.

If you want more practice than you can use this link.

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-graphically/e/graphing_systems_of_equations