Unit 6: Solving Systems of Equations Review

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

What are the characteristics of a one solution system of equations?

• The slopes and y-intercepts are the same.

• The slopes are the same and the y-intercepts are different.

• The slopes are different.

What are the characteristics of a no solution system of equations?

• The slopes and y-intercepts are the same.

• The slopes are the same and the y-intercepts are different.

• The slopes are different.

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

What are the characteristics of an infinitely many solutions system of equations?

• The slopes and y-intercepts are the same.

• The slopes are the same and the y-intercepts are different.

• The slopes are different.

Solve the system of equations using substitution, elimination, or inspection. Mark if the system will have one solution, no solution, or infinitely many solutions.

Groups:

(a) No Solution

,

(b) Infinitely Many Solutions

• 
• 
• 

A system of equations is shown. How many solutions does the system have, and why?

• There are no solutions because the slopes and y-intercepts are the same.

• There are infinitely many solutions because the slopes and y-intercepts are the same.

• There are no solutions because the slopes are the same and the y-intercepts are different.

• There are infinitely many solutions because the slopes are the same and the y-intercepts are different.

Select all the systems of equations that have exactly one solution. Select multiple answers.

• 
• 
• 
• 
• 

Casey orders 3 pizzas and 2 orders of breadsticks for a total of $29.50. Rachel orders 2 pizzas and 3 orders of breadsticks for a total of $23.

Write the equations (Example 4x+5y=12;4x+5y=12) No spaces

Using the equations from #7, solve the systems of equations. (Casey orders 3 pizzas and 2 orders of breadsticks for a total of $29.50. Rachel orders 2 pizzas and 3 orders of breadsticks for a total of $23.)