1. Activating Prior Knowledge – Notes
M4:LSN 29
Word Problems
Activating Prior Knowledge – Notes
Graph a system that has the following solutions.
One solution
No solutions
Infinite number
of solutions
Tie to LO

2. Learning Objective
Today, we will write and solve systems of equations from word problems.
CFU

3. Concept Development – Example #1
M4:LSN 29
Word Problems
Module 4
Page 172
Concept Development – Example #1
The sum of two numbers is 361 and the difference between the two numbers is What are the two numbers?
Let 𝑥= the first number, Let 𝑦= the second number
𝑥+𝑦=361
Use elimination to solve the system.
𝑥−𝑦=173
267+𝑦=361
2𝑥=534
− −267
𝑦=94
𝑥=267
The first number is 267 and the second number is 94.
CFU

4. Concept Development – Example #2
M4:LSN 29
Word Problems
Module 4
Page 172
Concept Development – Example #2
There are 356 Grade 8 students at Euclid’s Middle School. Thirty – four more than four times the number of girls is equal to half the number of boys. How many boys are in Grade 8 at Euclid’s Middle School? How many girls?
Let 𝑥= the number of boys, Let 𝑦= the number of girls
𝑥+𝑦=356
Use substitution to solve the system. Solve the second equation for 𝑥 by multiplying both sides by 2.
4𝑦+34= 1 2 𝑥
9𝑦+68=356
𝑥+32=356
2 4𝑦+34 = 1 2 𝑥 2
− −68
− −32
9𝑦=288
𝑥=324
8𝑦+68=𝑥
𝑦=32
8𝑦+68+𝑦=356
There are 324 boys and 32 girls at Euclid’s Middle School.
CFU

5. Concept Development – Example #3
M4:LSN 29
Word Problems
Module 4
Page 173
Concept Development – Example #3
A family member has some five – dollar bills and one – dollar bills in their wallet. Altogether she has 18 bills and a total of $62. How many of each bill does she have?
Let 𝑥= # of $5 bills, Let 𝑦= # of $1 bills
𝑥+𝑦=18
Use elimination to solve the system by subtracting the first equation from the second.
5𝑥+𝑦=62
−𝑥−𝑦=−18
11+𝑦=18
4𝑥=44
− −11
𝑦=7
𝑥=11
The family member has 11 $5 bills and 7 $1 bills in their wallet.
CFU

6. Closure –
1. What are the steps for solving a word problem using system of equations?
CFU