1. 5.4B Applying Systems Of Linear Equations
Algebra Glencoe McGraw-Hill J. Evans/C. Logan

2. Which method of solving systems of equations would be best to use?
1. The length of a rectangle is 2 m more than twice the width. The perimeter is 82 m. Find the dimensions of the rectangle.
Define Variables:
Let x = the width Let y = the length
Equations:
Which method of solving systems of equations would be best to use?
substitution
The width is 13 m
and the length is 28 m.

3. Which method of solving systems of equations would you use here?
2. The eighth grade class at LCMS has 335 students. Twice the number of girls is equal to three times the number of boys. How many boys and how many girls are in the class?
Define Variables:
Let g = # of girls Let b = # of boys
Verbal Model:
Equations:
# girls + # boys = total
2 X # of girls = 3 X # of boys
Which method of solving systems of equations would you use here?
substitution

4. combinations/elimination
3. The cost of 3 boxes of envelopes and 4 boxes of note paper is $ Two boxes of envelopes and 6 boxes of note paper cost $17. Find the cost of each box of envelopes and each box of note paper.
Define Variables:
Let e = cost of envelopes
Let n = cost of note paper
Verbal Model:
Equations:
3 X envelope cost + 4 X paper cost = $13.25
2 X envelope cost + 6 X paper cost = $17.00
Which method of solving systems of equations would you use here?
combinations/elimination

5. Which method of solving systems of equations would you use here?
4. Twenty pounds of dried fruit mix contained prunes worth $2.90 a pound and apricots worth $3.15 a pound. How many pounds of each did the mix contain if the total value of the mix was $59.75?
Define Variables:
Let p= amount of prunes Let a = amount of apricots
Verbal Model:
Equations:
amt. of prunes + amt. of apricots = Total amt.
prunes value + apricots value = mix value
Which method of solving systems of equations would you use here?
substitution

6. Which method of solving systems of equations would you use here?
5. Mr. Scott kept part of his $5000 savings in an account that earned 8% interest and the rest in an account that earned 12% interest. How much did he have in each account if his annual interest income from the total investment was $514.80?
Define Variables:
Let x= amount invested at 8%; Let y = amount invested at 12%
Verbal Model:
Equations:
$ at 8% + $ at 12% = total $
interest interest
from 8% from 12% = total interest account account
Which method of solving systems of equations would you use here?
substitution

7. Try this one on your own:
6. The sum of two numbers is Five times the smaller number is 8 more than the larger number. What are the two numbers?
The numbers are 18 and 82.

8. There are 134 boys and 201 girls at the school.
#2. Solve the second equation for g.
You’ve found the number of boys at the school. Use that information to determine the number of girls.
There are 134 boys and 201 girls at the school.

9. Note paper costs $2.45 and envelopes cost $1.15.
#3. What could you multiply each equation by to eliminate one of the variables?
If boxes of note paper cost $2.45 each, how much do boxes of envelopes cost?
Note paper costs $2.45 and envelopes cost $1.15.

10. There were 7 lb. of apricots and 13 lb. of prunes in the mix.
#4. Solve the first equation for one of its variables.
If the mix contained 7 lb. of apricots, how many pounds of prunes did it contain?
There were 7 lb. of apricots and 13 lb. of prunes in the mix.

11. He had $2130 invested at 8% and $2870 invested at 12%.
#5. Solve the first equation for one of its variables.
If Mr. Scott had $2130 in the 8% account, how much was in the 12% account?
He had $2130 invested at 8% and $2870 invested at 12%.