Linear Systems

One brand of suntan lotion comes in a small size with x ounces of lotion and a regular size with y ounces of lotion. Two small bottles plus one regular bottle contain 15 ounces of lotion, while one small bottle and two regular bottles contain 19.5 ounces of lotion. How much lotion is contained in the small bottle?

• 5 ounces

• 3.5 ounces

• 8 ounces

• 6.5

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

What is the solution to this system?

• (-2, -2)

• (2, -2)

• (-2,2)

• (2, 2)

Solve for x and y:
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Solve the system of equations.
x + 2y = -3
x - y = -12

• (-9, 3)

• (-7 ,5)

• (3, 15)

• (9, 6)

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

What is a solution of a linear system?

• the slope of the line

• the y-intercept

• the point where the systems intersect

• the rise over tun

Solve:
x + y = 4
-5x - 6y = -18

• (6, -2)

• (-6, 10)

• (2, 2)

• (-2, 6)

Solve:
-2x + 5y = -1
4x - 2y = -6

• (-2, -1)

• (2, 7)

• (3, 1)

• (-1, -2)

What is a solution of a linear system if the lines are the same?

• One solution

• No solution

• Infinitely Many solutions