One Solution, No Solution and Many Solutions

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Tags

CCSS.8.EE.C.8A

Based on the equations for each line, determine how many solutions the system would have.

y=2x+3

y=-4x+3

• Infinite Number of Solutions

• No Solution

• One Solution

Tags

CCSS.8.EE.C.8B

Based on the equations for each line, determine how many solutions the system would have.

y=5x+3

y=5x-2

• Infinite Number of Solutions

• No Solution

• One Solution

Tags

CCSS.8.EE.C.8B

Based on the equations for each line, determine how many solutions the system would have.

y=-3x+2

y=-3x+2

• Infinite Number of Solutions

• No Solution

• One Solution

Tags

CCSS.8.EE.C.8B

What is the solution to this equation?

• one solution

• no solution

• infinite solutions

• none of these

Tags

CCSS.8.EE.C.7A

What is the definition of one solution?

• There will only be ONE number that will make both sides equal.

• Any value for the variable can be substituted and both sides will NEVER be equal.

• Any value for the variable can be substituted and both will sides will ALWAYS be equal.

Tags

CCSS.8.EE.C.7A

What the is the definition of no solution?

• Only 1 value for the variable will make both sides equal.

• No matter how many different numbers you substitute for the variable, both sides will NEVER be equal.

• You can put any number in for the variable and both sides will always be EQUAL.

Tags

CCSS.8.EE.C.7A

Solve:
3x + 15 = 3(x + 5)

• No Solution

• x = 15

• Infinitely Many Solutions

Tags

CCSS.8.EE.C.7A

Solve:
2x + 1 = 2x - 1

• No Solution

• x = 0

• Infinitely Many Solutions

Tags

CCSS.8.EE.C.7A

How many solutions? 4x - 3 = 3(2x + 3)

• one solution

• no solution

• infinitely many solutions

Tags

CCSS.8.EE.C.7A