Warmups – Solve using any method.
1)
y=x–6
3x – 2y = 7
2) x – y = 5
2x – 3y = 7
3) 4x + 5y = 12
4x + 3y = 4
Homework Questions?
Word Problems
Objective: To solve word
problems involving systems of
equations.
WORDS THAT MEAN . . .
ADD
SUBTRACT
MULTIPLY
Sum
Difference
Product
Plus
Minus
Times
Increased by Decreased by Twice (x2)
Subtracted
Added to
from
Switch
Order
More than
Less than
EXAMPLE 1
1) Two numbers have a sum of 25. One number is 5 more
than the other number. Find the numbers.
Pick 2 variables
x and y
Write 2 equations
x + y = 25
x=5+y
Solve using . . . substitution
5  y  y  25
2 y  5  25
2 y  20
y  10
Don’t forget, you get 2 answers: y = 10, x = 15
You do not have to write these as an ordered pair.
EXAMPLE 2
2) The difference of two numbers is 6. Their sum is 30.
Find the two numbers.
Pick 2 variables
x and y
Write 2 equations
x–y=6
x + y = 30
2 x  36
x  18
Solve using . . . elimination
Don’t forget, you
get 2 answers:
x = 18, y = 12
EXAMPLE 3
3) The sum of two numbers is 15. One number is 4 times
the other. Find the numbers.
Pick 2 variables
x and y
Write 2 equations
x + y = 15
x = 4y
Solve using . . . substitution
4 y  y  15
5 y  15
y3
Don’t forget, you
get 2 answers:
y = 3, x = 12
TOO:
1)
The sum of two numbers is 32. The difference
between the two numbers is 8. Find the numbers.
20, 12
1)
Three times the first number plus the second number
equals 20. Five times the first number minus the
second number equals 12. Find the numbers.
4, 8
HOMEWORK

Solving Problems with System of
Equations
 Do
both sides
 Tell me if you used substitution (S) or
elimination (E)
QUIZ next week  Yippee!