Solving System of Equations by Graphing

Solving System of Equations by Graphing

​Quiero que abra una nueva pestaña y abra Demos, para que pueda graficar las ecuaciones que le he proporcionado en las diapositivas.

I want you to open a new tab and open Demos, so that you can graph the equations I have provided for you on the slides.

Click here --> https://www.desmos.com ​

One Solution

Here the is one solution

We can solve system of equations. by graphing

The solution is where the two lines intersect

Many Solutions

• Same LIne

• Coinciding Lines

No solution

​

The lines will be parallel lines​.

Fill in the Blank

What is the solution to the system

y = x -8

y = -2x + 1

**Be sure your answer is an ordered pair with no spaces example (1,2)

Fill in the Blank

What is the solution to the system

$$y\ =\ \frac{1}{2}x+9$$  

$$y\ =\ -x\ +6$$   **Be sure your answer is an ordered pair with no spaces example (1,2)

Multiple Choice

What is the solution to the system below: $$y\ =\ \frac{1}{3}x\ +\ 1$$   $$y\ =\ 4x\ -10$$  

• (3, -2)

• (-3,2)

• (2,3)

• (3,2)

Fill in the Blank

What is the solution to the system: $$-2x+3y\ =\ -9$$   $$x\ +\ y\ =\ 2$$  

**Be sure your answer is an ordered pair with no spaces example (1,2)

Fill in the Blank

What is the solution to the system:

-3x + y = 8

-x + y = -2

**Be sure your answer is an ordered pair with no spaces example (1,2)

Multiple Choice

What is the solution to the system: $$x\ +\ 2y\ =\ 4$$   $$y\ =-\ \frac{1}{2}x\ +2$$  

**Be sure your answer is an ordered pair with no spaces example (1,2)

• infinite 

• (0, 2)

• no solution

• (2, 0)

Multiple Choice

What is the solution to the system below: $$x\ +\ 3y\ =\ -15$$  

$$y\ =\ -7$$   **Be sure your answer is an ordered pair with no spaces example (1,2)

• ( -6, -7) 

• (6, -7)

• ( -7, 6) 

• ( -7, -6) 

Multiple Choice

What is the solution to the system below: $$y\ =\ x\ +\ 5$$  

$$x\ -\ y\ =\ 2$$   **Be sure your answer is an ordered pair with no spaces example (1,2)

• infinite

• ( 5, 2) 

• ( 2, 5) 

• No solution

Fill in the Blank

Solve the system below:

3x - 5y = -35

2x + y = -6

**Be sure your answer is an ordered pair with no spaces example (1,2)

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

What is the solution to this system of equations?

• (4, -1)
• (-1, 4)
• (-4, 1)
• (-4, -1)

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Multiple Choice

The solution to this system of equations is:

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

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

How can I graph using the graphing calculator?

• ​Go to https://www.desmos.com and click on "Graphing"

• Input the equations into y =

• The equations need to be in y = form

• Next hit the graph key

• Hit trace, use the arrow keys to find the intersection

  ​

What is the solution to the equations

y = 2x

y = -2x + 1

• Input the equations into y =

• Graph it

• 2nd calc, 5 enter, enter, enter

• ON the bottom will be the intersection

YOUR TURN

Multiple Choice

Using desmos.com What is the solution to the equations

y = -2x + 6

y = 2x - 2

• (2, 2)

• (3, 3)

• (-3, 3)

Multiple Choice

Using Desmos.com What is the solution?

y = 3x

y = -x + 4

• (3, 1)

• (1, 3)

• (2, 4)

Multiple Choice

Using Desmos.com What is the solution to

y = 4x + 8

y = 4x -3

• many solutions

• (1, 2)

• No solution

Multiple Choice

Using Desmos.com Solve the following

y = -3x + 2

y = 2x - 3

• (-1, 1)

• (1, -1)

• (1, 1)