Fast Track - Systems of Linear Equations

If a system of equations has no solution, what does the graph look like? 

​ (a)  

• parallel lines
• intersecting lines
• same line
• perpendicular lines

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both company's pizza cost the same amount? 

• y = 6.80 + .65x
  y=7.30+.90x
• x + y = 6.80
  x + y = 7.30
• y = 6.80+.90x
  y = 7.30 + .65x
• y + .90x = 6.80
  y + .65x = 7.30

What steps do you take to graph a linear equation?

(Put them in correct order)

• Find the

  Y-intercept (0,b)

• Plot the Y-intercept

• Find the slope of our line (m)

• Use slope to create line

• Solve for Y-variable.

  (isolate Y)

This system has _____ solutions.

• 0
• 1
• 2
• Infinitely many

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Solve by elimination method.
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.   On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. 

Determine the cost of 1 cup of coffee? 

• Cost of 1 cup of coffee is $.80

• Cost of 1 cup of coffee is $1.18

• Cost of 1 cup of coffee is $1.25

• Cost of 1 cup of coffee is $1.75

The Maplewood Symphony Orchestra sold 146 tickets and collected a total of $1036 in ticket sales. Admission was $5 for children and $8 for adults. Write two equations that would be used to solve the system.

• c+a=146

  5c+8a=1036

• c-a=146

  8c+5a=1036

• c+a=1036

  8c+5a=146

• c+a=146

  5c-8a=1026

Solve by Substitution:

y = -6

-3x - 6y = 24

• (6, 6)

• (6, -6)

• (4, -6)

• (-6, 4)

• (-1,7) and (0,5)

• (-4,2) and (-5,8)

• (-2,6) and (10,15)

• (-2,4) and (6,12)