Write Systems of Linear Equations from Verbal, TEKS A.2I

A set of 2 or more equations with the same variables.

System of Equations:

Writing Systems from Word Problems:

• Cost of gas (dependent variable)

• Number of gallons of gas (independent variable)

​Example:

1.) Define the 2 variables using Let statements.

2.) Write the 2 equations.

​Steps:

Let Statements:

• Let x = Number of gallons of gas

• Let y = Cost of gas

Multiplication Key Words:

If you can tell that a number is being multiplied, then that number is your slope, m, because y = mx + b.

• ​Each

• Every

• Per

• Monthly/Hourly/Annually/Daily

• Of

• Rate/Rate of Change

Addition/Subtraction Key Words:

If you can tell that a number is being added or subtracted, then that number is your y-intercept, b, because y = mx + b.

• ​Starting point

• Initial value

• Add/plus

• Increase

• Together

• Deposit (+)

​Addition:

​Subtraction:

• ​Difference

• Less than

• Deduct/withdraw

• Decrease

• Left

• Remaining

• Discount

​Example:

​Example:

Multiple Choice

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

Multiple Choice

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x = Erin's age and y = Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

Multiple Choice

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Multiple Choice

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50
• 10c + 5d = 16.50
  5c + 10d = 14.25
• c + d = 10
  5c + 10d = 16.50
• c + d = 5
  5c + 10d = 16.50

Multiple Choice

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8
• t + n = 54
  n = 3t + 8
• t + n = 54
  t = 3n - 8
• t + n = 8
  t = 3n + 54

Multiple Choice

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 

• y = 9.65 + x
  y = 8.40 + x
• y = 9.65x + 43
  y = 8.40x + 58
• y =9.65x
  y = 8.40x
• y = 9.65x - 43
  y = 8.40x - 58

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x + 0.5y = 78.5
  x + y = 87

• 1.5x + 0.5y = 78.5
  1.5x + 0.5y = 87

• x + y = 78.5
  1.5x + 0.5y = 87

• x + y = 78.5
  x + y = 87

Multiple Choice

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.

• T + F = 1430
  20T + 50F = 49
• T+ F = 49
  10T + 5F = 1430 
• T + F = 49
  20T + 50F  = 1430
• T + F = 49
  T + F = 1430

Multiple Choice

There are 50 donkeys and chickens on a farm.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174
  4d + 2c = 50
• d + c = 50
  4d + 2c = 174
• d + c = 50
  2d + 4c = 174
• d + c = 174
  2d + 4c = 50

Multiple Choice

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x
• x + y = 1550
  y = x + 4
• y - x = 1550
  y = 4x
• y = 1550 + x
  y = x + 4

Poll

Are you Clear or Cloudy on this lesson?

• I'm Clear. I could teach this lesson to others.

• I'm Cloudy. I should re-do this lesson.