Download 13_01 - Using Systems - Number Problems

13.01
Using Systems
to solve
Word Problems
(Numbers)
A system of equations can be used
to solve various word problems.
To solve a word problem using a system:
1) read the problem carefully
2) assign variables to represent the unknowns
and set up a system using the information
from the problem
3) solve the system
4) answer the question and
check to see if the answer makes sense
Solve the following word problem.
One number is four more than another.
The sum of the numbers is 14.
Find the numbers.
Let:
x = 1st number
x = y + 4
x + y = 14
Solve the system
(y + 4) + y = 14
2y + 4 = 14
2y = 10
y = 2nd number
x = y + 4
x = 5 + 4
x = 9
y = 5
The numbers are 9 and 5
Solve the following word problem.
The sum of two numbers is fourteen.
The difference of the same two numbers is ten.
Find the numbers.
Let:
x = 1st number
x + y = 14
x – y = 10
____________
2x = 24
x = 12
y = 2nd number
Solve the system
x + y = 14
12 + y = 14
y = 2
The numbers are 12 and 2
Solve the following word problem.
The sum of two numbers is two.
The sum of twice the 1st number and five times
the 2nd number is one.
Find the numbers.
Let:
x = 1st number
x + y = 2
2x + 5y = 1
y = 2nd number
Solve the system
x + y = 2
– 2x – 2y = – 4
2x + 5y = 1
________________
x – 1 = 2
x = 3
3y = – 3
y = –1
The numbers are 3 and – 1
Solve the following word problem.
Four times x minus three times y equals seventeen.
Three times x plus 2 times y equals zero.
Find the numbers.
Let:
x = 1st number
4x – 3y = 17
3x + 2y = 0
y = 2nd number
Solve the system
3x + 2y = 0
12x – 9y = 51
– 12x – 8y = 0
________________
3x + 2(– 3) = 0
3x – 6 = 0
– 17y = 51
3x = 6
y = –3
x = 2
The numbers are 2 and – 3