Linear Equations (w. One variable) Types of Solution

Three Types of Linear Solution

There are 3 types of solutions

• one solution

• no solution

• infinite solutions

One Solution

• can be solved

• coefficients are different

• constants are the same

• usually ends with "x = a number"

No Solution

• coefficients are the same

• constants are always different

• usually ends with a false statement

• example " 7 = 5"

Infinite Solution

• coefficients are always the same

• constants are always the same (when simplified).

• usually ends with a true statement

• example " 5 = 5" or " a = a"

Multiple Choice

what is the solution of an equation says

y = 0

• one solution

• no solution

• infinite solution

Multiple Choice

 $3\left(4-5x\right)=2-15x$  

• No Solution

• Infinite Solutions

•  $x=14$  

•  $x=10$  

Multiple Choice

 $2\left(x-6\right)=2x-12$  

• No Solution

• Infinite Solutions

•  $x=8$  

•  $x=-8$  

Multiple Choice

 $-2x+5=-2x+5$  

• No Solution

• Infinite Solutions

•  $x=10$  

•  $x=-20$  

Multiple Choice

what is the solution of an equation says

7 = 7

• one solution

• no solution

• infinite solution

Multiple Choice

 $7x-3=7x+15$  

• No Solution

• Infinite Solutions

•  $x=2$  

•  $x=8$  

Multiple Choice

 $-24+20x=24+8x$  

•  $x=4$  

•  $x=-2$  

• No Solution

• Infinite Solutions

Multiple Choice

what is the solution of an equation says

6 = -6

• one solution

• no solution

• infinite solution

Multiple Choice

what is the solution of an equation says

x=x

• one solution

• no solution

• infinite solution

Multiple Choice

 $7x-3=-3+7x$  

• No Solution

• Infinite Solutions

•  $x=0$  

•  $x=6$  

Multiple Choice

 $5\left(2+x\right)=45+5x$  

• No Solution

• Infinite Solutions

•  $x=35$  

•  $x=55$  

Graph of Solutions

The graph of each solution type is distinct

Multiple Choice

If a linear equation has infinitely many solutions, what does this mean about the two lines?

• Intersecting lines

• Identical line

• Parallel lines

Multiple Choice

The solution to this system is:

• No solution
• (0, 1)
• (0, -2)
• (4, 3)

Multiple Choice

What type of solution does the following represent?

• one solution

• no solution

• infinite solution

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

What type of solution does the following system represent?

• one solution

• no solution

• infinite solution