System of Equations

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

What is the solution to this system?
x= 7 - 2y
2x + y = 5

• (-1,4)

• (4,-1)

• (1,3)

• (3,1)

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

-4x-2y=-12
4x+8y=-24

• (5,6)

• (6,-6)

• (6,-2)

• (4,-3)

4x+8y=20
-4x+2y=-30

• (-7,1)

• (2,-5)

• (-2,5)

• (7,-1)

−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

-4x - 6y = 6
4x + 6y = -4

• no solution

• (2,0)

• (-4,0)

• (0,0)

This system has _____ solutions

• no

• 1

• 2

• Infinitely many

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution

• No solution

• Infinitely Many Solutions

2x - y = 0

4x - y = 0

• (1,2)

• (0,0)

• No Solutions

• Infinite Solutions