Linear Systems ~ Real World Applications - 10?s

What is the 1st step to solving a real-world application problem of systems?

• Solve the system using the Substitution or Elimination

• Write 2 linear equations to create a system

• Define the variables (x and y)

• Write answers with labels (in context of the problem)

TRUE or FALSE:

Defining the variables for a system means to describe in words what the x and y represent for the problem.

• TRUE

• FALSE

TRUE or FALSE:

You can only use the Elimination method to solve a real-world application of systems problem.

• TRUE

• FALSE

Which methods can be used to SOLVE a systems application problem?

• Graphing method

• Substitution method

• Elimination method

• None of these methods

1) Define the variables for the system:

At Sam’s pizza a soda and 2 slices of everything pizza cost $10.25.  At Two Cousin’s a soda and 4 slices of everything pizza cost $18.75.  What is the cost for a soda and a slice of pizza?

• x = # of sodas purchased

  y = # of slices of pizza purchased

• x = cost of a soda

  y = cost of a slice of pizza

• x = Sam's Pizza

  y = Two Cousin's

1) WRITE 2 EQUATIONS for the SYSTEM:

At Sam’s pizza a soda and 2 slices of everything pizza cost $10.25.  At Two Cousin’s a soda and 4 slices of everything pizza cost $18.75.  What is the cost for a soda (x) and a slice of pizza (y)?

• x = 10.25

  y = 18.75

• x + 2y = 18.75

  x + 4y = 10.25

• 2x + y = 10.25

  4x + y = 18.75

• x + 2y = 10.25

  x + 4y = 18.75

1) SOLVE the SYSTEM:

At Sam’s pizza a soda and 2 slices of everything pizza cost $10.25.  At Two Cousin’s a soda and 4 slices of everything pizza cost $18.75.  What is the cost for a soda (x) and a slice of pizza (y)?

• The cost of a soda is $1.75.

  The cost of a slice of pizza is $4.25.

• The cost of a soda is $4.25.

  The cost of a slice of pizza is $1.75.

• The cost of a soda is $10.25.

  The cost of a slice of pizza is $18.75.

2) Define the variables

Eden sold 11 packages of sugar cookie dough and 3 packages of oatmeal cookie dough for a total of $208.  Danna sold 1 package of sugar cookie dough and 14 packages of oatmeal cookie dough for a total of $266.  What is the cost of one package of sugar cookie dough and one package of oatmeal cookie dough?

• x = # of packages of sugar cookie dough

  y = # of packages of oatmeal cookie dough

• x = cost of a package of sugar cookie dough

  y = cost of a package of oatmeal cookie dough

• x = amount of money Eden made fundraising

  y = amount of money Danna made fundraising

• x = sugar cookie dough

  y = oatmeal cookie dough

2) Write TWO equations of the system

Eden sold 11 packages of sugar cookie dough and 3 packages of oatmeal cookie dough for a total of $208.  Danna sold 1 package of sugar cookie dough and 14 packages of oatmeal cookie dough for a total of $266.  What is the cost of one package of sugar cookie dough (x) and one package of oatmeal cookie dough (y)?

• 11x + 3y = 208

  x + 14y = 266

• x + 3y = 208

  11x + 14y = 266

• x + y = 208

  x + y = 266

• 3x + 11y = 208

  14x + y = 266

2) SOLVE the system

Eden sold 11 packages of sugar cookie dough and 3 packages of oatmeal cookie dough for a total of $208.  Danna sold 1 package of sugar cookie dough and 14 packages of oatmeal cookie dough for a total of $266.  What is the cost of one package of sugar cookie dough (x) and one package of oatmeal cookie dough (y)?

• One package of sugar cookie dough is $18.

  One package of oatmeal cookie dough is $14.

• One package of sugar cookie dough is $14.

  One package of oatmeal cookie dough is $18.

• One package of sugar cookie dough is $15.

  One package of oatmeal cookie dough is $17.

• One package of sugar cookie dough is $208.

  One package of oatmeal cookie dough is $266.