Apply Systems of Equations

A system of equations with infinitely many solutions will have lines that...

• are the same

• are parallel and never touch

• cross in one place

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

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

This system has _____ solution(s).

• 0

• 1

• 2

• Infinitely many

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.  What is the solution?

• (3, -2)

• (3, -3)

• (-3, 2)

• (-3, -3)

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 

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 the system of equations?

• No Solution

• (2, 0)

• Infinitely Many Solutions

• (0, 2)

What is the solution to the system of equations?

• (-1, -3)

• (3, 1)

• (1, 3)

• (-3, -1)

What is the solution to the system of equations?

• No Solution

• Infinitely Many Solutions

• (7, -2)

• (-5, -5)