1. 7.4 Applications of Linear Systems
Algebra
7.4
Applications of
Linear Systems

2. There are 3 methods for solving systems of equations
There are 3 methods for solving systems of equations. The method you choose should be which one is the easiest in the given case.
Let’s briefly review each method.

3. The solution is the point of intersection of the two graphed lines.
1. Graph and Check Method
The solution is the point of intersection of the two graphed lines.
To solve:
Graph both equations
Identify intersection point (x,y)
Plug in to original equations to check

4. 2. Substitution Method 3x + y = 5 y = 5 – 3x 2x – y = 10 2x – ( ) = 10
The solution is (3, - 4)
x = 3

5. Linear Combinations Method
6x + 6y = 18
[ ] 2
3x + 3y = 9
5x + 2y = 12
-15x - 6y = -36
[ ]-3
-9x = -18
x = 2 2
3x + 3y = 9
3(2) + 3y = 9
Solution: (2, 1)
6 + 3y = 9
3y = 3
y = 1

6. When to Use Which Method
Graphing: When the equation is already graphed and the intersection (x,y) is whole numbers
Substitution: When one variable is already isolated
Linear combinations: No variable has coefficient of 1 or -1 and columns are lined up

7. Which method would you use?
8x + y = 24
6x – y = 18
Linear combinations
x = 2y + 4
2x - 6y = 12
Substitution
Either
x + y = 12
6x + y = 32

8. Set-up for Mixture Problems
Write one equation to describe
QUANTITY.
Write other equation to describe
VALUE.

9. Set up a system and solve the mixture problem.
You exercised on a treadmill for 3 hours. You ran at 4 miles per hour, then you sprinted at 6 miles per hour. If the treadmill monitor says that you ran and sprinted 14 miles, how long did you run at each speed?
Let x be the # of hours you ran at 4 mph
Let y be the # of hours you sprinted at 6 mph
Quantity: x + y = 3
Value: 4x + 6y = 14
You ran (x) for 2 hours and you sprinted (y) for 1 hour.
Now, you solve.

10. Set up a system and solve the mixture problem.
A store sold 28 pairs of running shoes for a total cost of $2220. Nikes sold for $70 per pair and Asics sold for $90 per pair. How many of each style were sold?
Let x be the # of Nikes sold
Let y be the # of Asics sold
Quantity: x + y = 28
Value: 70x + 90y = 2220
The store sold 15 pairs of Nikes and 13 pairs of Asics.
Now, you solve.

11. Together from the Homework
pg #43, 47

12. Homework
pg #25 – 45 odd,