MPM2D
U01L06
Solving Word Problems using Linear Systems - Day 1
To solve a word problem there are four important steps;
• Define your variables (let statements, one for each variable)
• Create two equations using your two unknown quantities
• Solve using the method of your choice (graphing or algebraically)
• Concluding Statement (related to the problem)
• Verify (optional)
Example #1: Write an equation for each situation below using the given let statements.
Let x represent the larger of the two unknown numbers.
Let y represent the smaller of the two unknown numbers.
a)
The sum of the two numbers is negative five.
b)
The difference between the larger number and the smaller is twelve.
Three times the smaller number subtracted from twice the larger gives a result
c)
of nine.
d)
The sum of half the larger number and one-third the smaller number equals seven.
Example #2: Find two numbers with a sum of -6 and a difference of 34.
Step 1: Define your variables
Let x represent one of the unknown numbers.
Let y represent the other unknown number.
Step 2: Create two equations using your two unknowns
Step 3: Solve using the method of your choice.
Using the method of elimination; (1) + (2)
Substitute x = 14 into (1)
Step 4: Concluding Statement
Therefore one of the numbers is 14 and the other is ­20.
MPM2D
U01L06
Example # 3: The sum of two numbers is 12. Twice the larger plus
the smaller equals 21. Find the two numbers?
Step 1: Define your variables
Let x represent the larger number.
Let y represent the smaller number.
Step 2: Create two equations using your two unknowns
Step 3: Solve using the method of your choice
Using elimination, equation (2) ­ equation (1)
Substitute x = 9 into (1)
Step 4: Concluding Statement
Therefore the larger number is 9 and the smaller number is 3.
Example # 4: Find two numbers such that one-half their sum is 11
and one-third their difference is 2.
Let x represent one of the numbers
Let y represent the other number
Using elimination, equation (3) + equation (4)
Substitute x = 14 into equation (1)
Therefore one of the numbers is 14 and the other is 8.
Homework: p. 51 # 7 , 8 , 12 , 22
p. 53 # 32
p. 103 # 18
p. 104 # 24