Classifying Systems of Equations lesson

Solving Systems of Equations by Graphing

Math 8 with Mrs. Booker

We can solve the system of equation by graphing each equation and finding their intersection point.

• y = 2x + 3

• y = -3x + 4

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

One Solution

When you graph both equations they will cross in exactly ONE POINT. The INTERSECTION POINT is the ANSWER to the system.


Classification:
Consistent Independent System

No Solution

When you graph both equations they NEVER intersect. No intersection point means no solution.

Classification:
Inconsistent Independent System

Infinite Solutions

When you graph both equations and they overlap. When the lines overlap at every point it means they have infinite solutions. They are actually the same line.

Classification:
Consistent Dependent System

Multiple Choice

If you graph 2 lines and they intersect at ONE point, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None of These

Multiple Choice

If 2 lines never intersect, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None Of These

Multiple Choice

If a system has 2 lines that overlap, meaning they share all of the same points, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None Of These

Multiple Choice

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE
• FALSE

Multiple Choice

What is the first step in solving a system by graphing?

• Write both linear equations in slope-intercept form
• Get x by itself
• Compare the slopes of both equations
• Write both equations in standard form

Multiple Choice

A system of linear equations is... 

• Math Magic
• One Equation
• Always more than 2 equations
• A set of 2 or more equations

Multiple Choice

Classify the system:

y = ²/₃x + 6

y = ²/₃x + 6

• Consistent Independent

  (one solution)

• Consistent Dependent

  (infinite solutions)

• Inconsistent

  (no solutions)

Multiple Choice

Classify the system:

y = ¹³/₈x + 7

y = ¹/₈x - 5

• Consistent Independent

  (one solution)

• Consistent Dependent

  (infinite solutions)

• Inconsistent

  (no solutions)

Multiple Choice

Classify the system:

y = ⁵/₄x + 9

y = -³/₂x + 9

• Consistent Independent

  (one solution)

• Consistent Dependent

  (infinite solutions)

• Inconsistent

  (no solutions)

Multiple Choice

Classify the system:

y = -2x + 7

y = -2x + 9

• Consistent Independent

  (one solution)

• Consistent Dependent

  (infinite solutions)

• Inconsistent

  (no 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

Multiple Choice

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution. 
• you will have one solution.
• you will have infinite solutions. 
• you will graph a giraffe. 

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Multiple Choice

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution
• No solution
• Infinitely Many Solutions

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

Multiple Choice

Lesly graphed two lines in order to find the solution to a given system of equations.

What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Multiple Choice

These two lines intersect at _____.

• (4, -2)

• (4, 2)

• (-2, 4)

• No solution

Multiple Choice

The solution to this system of equations is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution