Substitution - Systems of Equations

Substitution - Systems of Equations

Fabulously Fit offers memberships for $35 per month plus a $50 enrollment fee. The Fitness Studio offers memberships for $40 per month plus a $35 enrollment fee.

In how many months will the fitness clubs cost the same?

What will the cost be?

Multiple Select

Fabulously Fit offers memberships for $35 per month plus a $50 enrollment fee. The Fitness Studio offers memberships for $40 per month plus a $35 enrollment fee. In how many months will the fitness clubs cost the same? What will the cost be?

What are the x and y variables? (click both that apply)

• x = number of months

• y = enrollment fee

• x = price per month

• y = total cost

Multiple Choice

Fabulously Fit offers memberships for $35 per month plus a $50 enrollment fee. The Fitness Studio offers memberships for $40 per month plus a $35 enrollment fee. In how many months will the fitness clubs cost the same? What will the cost be?

What is the Fabulously Fit equation?

• $y=50x+35$

• $y=35x+50$

• $y=35x+40$

• $y=40x+35$

Multiple Choice

Fabulously Fit offers memberships for $35 per month plus a $50 enrollment fee. The Fitness Studio offers memberships for $40 per month plus a $35 enrollment fee. In how many months will the fitness clubs cost the same? What will the cost be?

What is the Fitness Studio equation?

• $y=50x+35$

• $y=35x+50$

• $y=35x+40$

• $y=40x+35$

Multiple Choice

The system of equations is: 

$$y=35x+50$$   $$y=40x+35$$   Substitute the first equation into the second equation.

• 35x + 50 = 40x + 35

• y = 40(35x + 50) +35

• y = 35(40x + 35) +50

Multiple Select

 $35x+50=40x+35$ 

What is the value of x? Check all that apply.

• x = 3

• x = 5

• 3 months

• $5

Multiple Select

Substitute x = 3 into one of the equations.

 $y=35x+50$  
 $y=40x+35$  

What is the value of y? Check all that apply.

• y = 120

• y = 155

• $120

• $155

Solution

It will take 3 months for the total cost of each gym membership to equal $155.

The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 cm. What are the rectangle's dimensions?

Poll

What is the formula for perimeter?

• $2l+2w=P$

• $l\times w=P$

• $2l\times2w=P$

• $l+w=P$

Multiple Select

The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 cm. What are the rectangle's dimensions?

What are the two variables? Check all that apply.

• 
  

  $l\$ = perimeter

• $l$ = length

• $w$ = width

• $w$ = cm

Multiple Select

The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 cm. What are the rectangle's dimensions?

What are the two equations? 

•  $lw=58$  
  

•  $w=3l$  
  

• 
  

   $l=w+3$  

•  $2l+2w=58$  
  

Multiple Choice

The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 cm. What are the rectangle's dimensions?

Which equation do we want to substitute into the other?

• Substitute $l=w+3$ into $2l+2w=58$

  
  

• Substitute $2l+2w=58$ into $l=w+3$

Fill in the Blanks

We substituted  $l=w+3$   into  $2l+2w=58$ . Now we solve for our remaining variable, w. What is the value of w?

Fill in the Blanks

Plug 13 back into EITHER equation to find the length:

 $l=w+3$  

 $2l+2w=58$  

What is the value of  $l$ ?

Solution

The rectangle has a length of 16 cm and width of 13 cm.