Applications of Linear Systems: Standard Form

Multiple Choice

Choose the equation that represents STANDARD FORM

• y = mx + b

• Ax + By = C

• y - y1 = m(x - x1)

• y = Ax + By

Multiple Choice

Which equation is written in STANDARD form?

• y = 1/2x + 2

• y - 3 = -5(x + 2)

• 7x + 2y = 9

• 3x + 2 = y

​Warm-Up
&
Review

Multiple Choice

5x + y = 4

6x + 2y = 1

Explain how to achieve COMMON COEFFICIENTS in the system.

Common Coefficients: opposite numbers OR the same numbers

• Multiply the TOP equation by 2 or -2.

• Multiply the TOP equation by 6 or -6.

• Multiply the BOTTOM equation by 5 or -5.

• Multiply the BOTTOM equation by 4 or -4.

Multiple Choice

Choose one way to achieve common coefficients in the system.

6x + 3y = 5

5x - 4y = 10

• Multiply the top equation by 6 and the bottom by 5.

• Multiply the top equation by 3 and the bottom by -4.

• Multiply the top equation by 4 and the bottom by 3.

• Multiply the top equation by -5.

Multiple Choice

Choose the strategy to solve the system by elimination.

-15x - 4y = 11

5x + 4y = -14

• Add to eliminate y

• Add to eliminate x

• Subtract to eliminate y

• Subtract to eliminate x

• none of these

Page 25 - Unit 6

​Oil Change Problem

Multiple Choice

DEFINE THE VARIABLES.

The total charge for an oil change at a service center includes a fee (x) for the oil change service and the cost of oil. Each quart of oil costs y dollars.

• x = oil change fee

  y = Cost for 1 quart of oil

• x = Cost for 1 quart of oil

  y = oil change fee

• x = total charge for the oil change

  y = # of quarts of oil

Multiple Choice

WRITE AN EQUATION.

The RED car required 7 quarts of oil. The total cost of the oil change was $66.35.

x = oil change fee

y = Cost for 1 quart of oil

• $$7x+y=66.35$$  

• $$x+y=66.35$$  

• $$x+7y=66.35$$  

Multiple Choice

WRITE AN EQUATION.

The BLUE car required 5 quarts of oil. The total cost of the oil change was $55.39.

x = oil change fee

y = Cost for 1 quart of oil

• $$5x+y=55.39$$  

• $$x+5y=55.39$$  

• $$y=5x+55.39$$  

Multiple Choice

$$x+7y=66.42$$  

$$x+5y=55.39$$  

What strategy could be used to solve the system?

• Subtract to eliminate x.

• Add to eliminate x.

• Subtract to eliminate y.

• Add to eliminate y.

Multiple Choice

$$x+7y=66.35$$  

$$x+5y=55.39$$  

Subtract and solve for y.

• $$12y=121.78$$  

  $$y=10.15$$  

• $$2y=121.78$$  

  $$y=60.89$$  

• $$2y\ =\ 10.96$$  

  $$y=5.48$$  

Multiple Choice

$$x+7y=66.35$$  

$$x+5y=55.39$$  

$$y\ =\ 5.48$$  

Solve for x.

•  

  $$x=27.99$$   

•  

  $$x=9.98$$   

• $$x=8.84$$  

Multiple Choice

Interpret the solution.

x = 27.99, y = 5.48

• The fee for an oil change is $5.48 and the cost for oil is $27.99.

• The fee for an oil change is $27.99 and the cost per quart of oil is $5.48.

• The total cost of an oil change is $27.99.

Page 26 Problem #1

​

​The Culinary Shop

Multiple Choice

Write a system to represent Problem #1 on page 26.

• $$2x+2y=176.50$$

  $$x+3y=163.25$$

• $$2x+2y=176.50$$

  $$3x+y=163.25$$

• $$2x+2y=163.25$$

  $$x+3y=176.50$$

Open Ended

Explain how you would multiply one or both equations to achieve common coefficients.

$$2x+2y=176.50$$

$$x+3y=163.25$$

Page 26, Problem #2

​Water

Wizz

Multiple Choice

Write a system of equations to represent problem #2 on page 26.

• $$5c+22s=1090$$

  $$3c+15s=735$$

• $$5x+22y=1090$$

  $$3x+15y=735$$

• $$5c+22s=735$$

  $$3c+15s=1090$$

Open Ended

Explain how to multiply and achieve common coefficients.

$$5c+22s=1090$$

$$3c+15s=735$$