Systems of Linear Systems

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Solve the following system:
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

Solve the following system by graphing.  What is the solution?

• (3, -2)

• (3, -3)

• (-3, 2)

• (-3, -3)

Solve the system using substitution.
16x + 2y = 2
y = -8x - 1

• (2,3)

• (-3,7)

• No Solution

• Infinitely Many Solutions

Solve the following system by graphing.  What is the solution?

• (-4, 2)

• (4, 2)

• (2, -4)

• (2, 4)

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?

• One Solution

• No solution

• Infinitely Many Solutions

One brand of suntan lotion comes in a small size with x ounces of lotion and a regular size with y ounces of lotion.  Given the equations below how can we eliminate the terms with x?
x+2y = 15
2x + y = 19.5

• subtract the two equations from each other

• multiply the second equation by -1 and add the two equations

• multiply first equation by 2, multiply the second equation by 1 then add them

• multiply the first equation by -2 then add the equations together 

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