Applications of Systems (LT 14)

What is the 1st step to solving a systems of equations word problem?

• 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:

When writing system of equations, they will be written in either Slope-Intercept form (y = mx + b) or Standard form (Ax + By = C)

• TRUE

• FALSE

Which of the following is Slope-Intercept form?

• Ax + By = C

• y = mx + b

TRUE or FALSE:

When SOLVING a system of equations, you can CHOOSE to use either Substitution method or Elimination method.

• TRUE

• FALSE

Step 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

Step 2) 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

• y = 2x + 10.25

  y = 4x + 18.75

• x + 2y = 10.25

  x + 4y = 18.75

Step 3) SOLVE the SYSTEM:

x + 2y = 10.25

x + 4y = 18.57

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.

Step 1) Define the variables

Eden sold 11 packages of sugar cookies and 3 packages of oatmeal cookies for a total of $208.  Danna sold 1 package of sugar cookies and 14 packages of oatmeal cookies 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 sold

  y = # of packages of oatmeal cookies sold

• x = cost of a package of sugar cookies

  y = cost of a package of oatmeal cookies

• x = amount of money Eden made fundraising

  y = amount of money Danna made fundraising

• x = # of cookies sold

  y = total amount of money earned

Step 2) Write TWO equations of the system

Eden sold 11 packages of sugar cookies and 3 packages of oatmeal cookies for a total of $208.  Danna sold 1 package of sugar cookies and 14 packages of oatmeal cookies 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

Step 3) SOLVE the system

11x + 3y = 208

x + 14y = 266

What is the cost of one package of sugar cookies (x) and one package of oatmeal cookies (y)?

• 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.