Multiples of Equations

Systems of equations

How to determine if systems have 1 solution, infinite soultions, or no solution.

If variables AND numbers in the equations are multiples of another another, then the solution is INFINITE!

 $4x\ +\ 2y\ =\ 10,\ 2x\ +\ y\ =\ 5$  

Multiple Select

Which equations are multiples of one another?

• x + 2y = 8

  3x - 9y = 6

• 4x + y = -8

  8x + 2y = =-16

• x - 5y = 3

  -2x + 10y = -6

• 8x - 5y = 12

  -3x - 4y = -3

If ONLY the variables are multiples of one another, then the answer is NO SOLUTION

 $x\ -3y\ =\ 2,\ -4x\ +\ 12y\ =\ 5$  

Multiple Select

Which equations has variables that are multiples ONLY?

• 5x + y = 3

  2x - 7y = 9

• 5x - 3y = 10

  -10x +6y = 0

• 4x + 8y = -10

  2x + 4y = -5

• -x - 2y = 11

  -2x - 4y = -7

If the variables ARE NOT mutltiples of one another, then there is ONE SOLUTION

 $4x\ -\ 3y\ =\ -2\ ,\ -5x\ +9y\ =\ 14$  

Multiple Select

Which equations are NOT multiples of one another of any kind?

• x - 3y = 2

  4x - 12y = -4

• 4x - 2y = 2

  -6x + 3y = -3

• 5x + 9y = 1

  -3x + y = -14

• x - y = 5

  x + y = 6

Multiple Choice

Which system has INFINITE SOLUTIONS

• 6x + 2y = -8

  5x + 10y = -15

• -5x - 10y = -15

  x + 2y = 5

• -9x + y = 5

  -18x + 2y = 0

Multiple Choice

Which system only has ONE solution?

• 7x - y = 2

  -7x + y = 40

• 3x + 2y = 10

  6x - 5y = 20

• 8x + 6y = -20

  -4x - 3y = -10

Multiple Choice

Which of the following systems has NO solutions?

• 6x - 8y = 2

  15x - 20y = 17

• 3x - 7y = - 5

  -3x +4y = 2

• x - y = 2

  -5x - 5y = 10

Poll

Which type of problem do you feel is the hardest to identify?

• Infinite Solutions

• No Solution

• ONE solution

• Some or all of them