Systems of Equations Graphing

Systems of Equations

​The graphing method

Poll

I am looking to work out more this year. Which gym should I join?

• Gym #1: $20 joining fee plus $10 a month

• Gym #2: $0 joining fee plus $15 a month

Multiple Choice

Gym #1: $20 joining fee plus $10 a month

Gym #2: $0 joining fee plus $15 a month

Which gym costs less after 3 months?

• Gym #1

• Gym #2

Multiple Choice

Gym #1: $20 joining fee plus $10 a month

Gym #2: $0 joining fee plus $15 a month

Which gym costs less after 6 months?

• Gym #1

• Gym #2

Fill in the Blanks

Gym #1: $20 joining fee plus $10 a month

Gym #2: $0 joining fee plus $15 a month

After how many months will I spend the same amount of money?

What is a system of equations?

• A system of equations consists of two or more equations

• Ex 1: y = 3x + 5 & y = -4x - 2 

• Ex 2:  3x + 2y = 2 &  y = x + 5  

• Ex 3: y = 2^x & y = 4

Gym #1: $20 joining fee plus $10 a month

Gym #2: $0 joining fee plus $15 a month

Write the linear equation for this scenario.

y=20+10x
y=0+15x

Domain?
Range?

Solving Systems of Equations by Graphing

Students will solve systems of linear equations graphically and algebraically.

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

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

Multiple Choice

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

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

When you graph the exact same equation twice,

• you will have no solution.

• you will have one solution.

• you will have infinite solutions.

Multiple Choice

How many solutions does the system have?

• Zero/None Solutions

• One solution

• Infinitely Many Solutions

Solutions to a System

• The solution to a system of equations is an ordered pair (x, y) that makes BOTH equations true.

• Graphically, the solution is the point of intersection.

  
  

Solving Systems of Equations by Graphing

y=2/3 x
y=2x-4

TI 84 steps
1. Mode
GraphTable
StatDiagnostic ON
2nd Zoom Gridlines
2. y=
3. Graph
4. 2nd Trace 5 Enter Enter Enter

Multiple Choice

Write the equation of the line.

• y = -1/3x - 2

• y = 1/3x - 2

• y = 3x - 2

• y = -3x - 2

Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

Multiple Choice

The solution is:

• (4, 3)

• (3, 4)

• (-4, 3)

• No solution

Multiple Choice

What is the solution?

• (6, 3)

• (3, 6)

• (-6, 3)

• No solution

Multiple Choice

How many solutions will this system have? 

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

To find the point of intersection

1. y=

2. Graph

3. 2nd Trace 5 Enter Enter Enter

​

TI 84 Steps

Do this first every time you get the calculator
1. Mode
2, Graph Table Enter
3. StatDiagnostic ON
4. 2nd Zoom Gridline

Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

Systems of Equations Graphically

• A system of equations is two or more equations with the same variables.

• To solve a system of equations with two variables, find the ordered pair that SATISFIES all of the equations.

Multiple Choice

What is the solution to the following system of equations?

• (0,3)

• (-3, 1)

• (1, 3)

• Infinitely Many Solutions

• No Solution

Multiple Choice

What is the solutions to the following system of equations?

• (5,2)

• (2, 5)

• (0,3)

• Infinity Many Solutions

• No Solutions

Multiple Choice

How many types of solutions are there?

• One

• Two

• Three

Multiple Choice

Which solution type has the same slope and the graphs are parallel?

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

Which solution type has the same slope and same y-intercept?

• No Solution

• One Solution

• Infinitely Many Solutions

Multiple Choice

Which solution type has it where the graphs intersect at a single point?

• Infinitely Many Solutions

• One Solution

• No Solution

Exit Ticket

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Multiple Choice

What is the solution of the two linear equations shown?

• (2,2)
• (0,0)
• (1,2)
• None of these

Multiple Choice

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)
• (0,-3)
• (3,0)
• (-3,0)

Fill in the Blanks

y=3x-5

y=2/3x+2