1. Solving System of Equations Word Problems

2. Table of Contents Pg
Title
LI/SC
Word Problem Notes

3. Learning Intention/Success Criteria
LI: We are learning how to solve a system of equations from word problems SC: I know how to -determine if a system of equations has many solutions -determine if a system of equations has one solution -determine if a system of equation has no solutions -solve systems of two linear equations algebraically using the elimination -solve systems of two linear equations algebraically using substitution -solve systems of two linear equations graphically using graphing -write linear equations from word problems

4. How to write equations from word problems
1. Identify the variables
2. Set up the two equations for the system
3. Solve the system
4. Answer the question

5. Example 1: The sum of two numbers is 130 and their difference is 54
Example 1: The sum of two numbers is 130 and their difference is 54. What are the two numbers?
Step 1: ID the variables
m = the first number
n = the second number
Step 2: Set-up the equations
Sum of two numbers:
m + n = 130
Difference of two numbers:
m – n = 54

6. Step 3: Solve the system
m + n = m – n = 54 + + +
2m = 184
___ 2
___ 2
m = 92
m + n = m = 92
92 + n = 130
-92
-92
n = 38

7. Step 4: Answer the questions
The two numbers are: 92 and 38

8. Total number of baskets x + y = 10
Example 2: On January 18, 2019, Stephen Curry of the Golden State warriors a total of 10 baskets. All of the points he made were either 2-point or 3-point baskets. If he scored a total of 23 points in that game, how many of each type of basket did he make?
Step 1: ID the variables
x = two point baskets
y = three point baskets
Step 2: Set-up the eqs
Total number of baskets
x + y = 10
Total number of points
2x + 3y = 23

9. Step 3: Solve the system x + y = 10 2x + 3y = 23 x = 10 – y
2(10 – y) + 3y = 23
- y
- y 20
- 2y
+ 3y = 23
x = 10 – y
20 + 1y = 23
-20
-20
x + y = y = 3
y = 3
x + 3 = 10 -3 -3
x = 7

10. Step 4: Answer the questions
Stephen Curry scored 7 two-pointers and 3 three-pointers.