Section 7.4 (continued) Using systems to solve word problems
1.) Define 2 different variables.
2.) Set up 2 different equations based upon information in the problem.
3.) Solve.
Ex: Solve
The sum of 2 numbers is 64 and their differences is 36. What are the numbers?
x=1st number
y=2nd number
x+y=64
x-y=36
cancel out the y variable because one is negative and one is positive.
2x=100
x=50
Plug the answer into one of the equations.
x+y=64
50+y=64
y=14
Ex: I am looking for 2 unknown numbers whose difference is 3. 4 times the larger number plus twice the smaller is 60. What are the numbers.
x= larger number
y= smaller number
x-y=3------->2x-2y=6
4x+2y=60------->4x+2y=60
multiply the first equation by 2 so x turns to y becomes -2y and the cancel out.
66x=66
x=11
Plug the answer into one of the equations.
4x+2y=60
44+2y=60
Subtract 44 from both sides
2y=16
Divide both sides by 2.
y=8
Using systems to solve word problems
1.) Define 2 different variables.
2.) Set up 2 different equations based upon information in the problem.
3.) Solve.
Ex: Solve
The sum of 2 numbers is 64 and their differences is 36. What are the numbers?
x=1st number
y=2nd number
x+y=64
x-y=36
cancel out the y variable because one is negative and one is positive.
2x=100
x=50
Plug the answer into one of the equations.
x+y=64
50+y=64
y=14
Ex: I am looking for 2 unknown numbers whose difference is 3. 4 times the larger number plus twice the smaller is 60. What are the numbers.
x= larger number
y= smaller number
x-y=3------->2x-2y=6
4x+2y=60------->4x+2y=60
multiply the first equation by 2 so x turns to y becomes -2y and the cancel out.
66x=66
x=11
Plug the answer into one of the equations.
4x+2y=60
44+2y=60
Subtract 44 from both sides
2y=16
Divide both sides by 2.
y=8