Review All Methods of Solving Systems

System of Linear Equations (Introduction)

Solution to a System of Equations

• Graphically: where the two lines intersect

• There are 3 types of solutions as seen in the picture to the right!

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

Multiple Choice

What is the solution to this system?

• (1, -2)

• No Solutions

• Infinite Solutions

• (0, -3)

Multiple Choice

What is the solution for the system: (take out a piece of paper or write on a whiteboard! you never know if this question will show up on a test or quiz)

$$y=-2x+9$$  
$$y=4x-3$$  

• (2, 5)

• (3, 7)

• (1, -2)

• (0, 2)
  
  

Multiple Choice

What is the solution for the system: (take out a piece of paper or write on a white board! you never know if this question will show up on a test or quiz)

$$y=\frac{1}{2}x+2$$  
$$y=-x-1$$  

• (-2, 1)

• (2, 3)

• (4, 5)

• (3, 4)
  
  

Multiple Choice

Use elimination to find the solution for the system:

(take out a piece of paper or write on a white board! you never know if this question will show up on a test or quiz)

$$2x+y=25$$  
$$-2x+3y=-13$$  

• (11, 3)

• (5, 7)

• (3, 2)

• (0, 13)
  
  

Multiple Choice

Use substitution to find the solution for the system:
(take out a piece of paper or write on a white board! you never know if this question will show up on a test or quiz)

$$x=6y-11$$  
$$3x-2y=-1$$  

• (1, 2)

• (8, 7)

• (3, -1)

• (3, 0)
  
  

Multiple Choice

what is the variable that willl be "eliminated"?

5x - 4y = 11

5x + 4y = -14

• x variable

• y variables

• both variables

Multiple Choice

what is the resulting combined equation to the following system:

5x - 4y = 11

5x + 4y = -14

• 5x = -3

• 10y = -3

• 10x = -3

• 10x = -25

Multiple Choice

what is the resulting combined equation for the system below?

9x + y = 12

-9x + y = 6

• -18x = 18

• y = 18

• 2y= 18

• 18x + 2y = 18

Multiple Choice

what do you need to multiply the top equation by to make a zero pair:

5x - 2y = 11

-10x + 3y = -4

• 5

• -1

• 2

• -2

Multiple Choice

Solve the system:
2x + 3y = -2
3x - 2y = 23

(take out a piece of paper or write on a white board! you never know if this question will show up on a test or quiz)

• (5, -4)
• (-4, 5)
• (-5, 4)
• infinite solutions

Multiple Choice

Solve by elimination
-12x-4y= -8 
  -6x-2y= -4

(take out a piece of paper or write on a white board! you never know if this question will show up on a test or quiz)

• no solution 
• (0,0)
• infinite solutions 
• (4,0)