1. Solving Applications: Systems of Two Equations
Section 8.3
Solving Applications:
Systems of Two Equations

2. Structure
Most of the problems we will be seeing in this section we have solved before.
The only difference is the set up, in the past we created one equation with one unknown, now we are going to create two equations with two unknowns.
Therefore we can choose which method we want to use to solve the equation.

3. Translation Problem
Read the word problem and create two equations based on the keywords.

4. Translation Problem
To make the problem seem less overwhelming find the equal sign. This will split the one word problem into two parts.

5. Example
A board 10 ft long is cut into two pieces. Three times the length of the shorter piece is twice the length of the longer piece. Find the length of each piece.

6. Mixture Problem Mixture of Money Mixture of Percent A * C = V
A = Amount = how mach have/need
C = Cost = how much per item
V = Value = how much total
Mixture of Percent
A * P = Q
A = Amount = how much you have/need
P = Percent = convert to decimal
Q = Quantity = how much you have from that percentage

7. Example – Mixture Money
Quick Copy recently charged $0.49 per page for color copies and $0.09 per page for black and white copies. If Shirley's bill for 90 copies was $12.90, how many copies of each type were made?

8. Example – Mixture Percent
Stacey's two student loans totaled $12, One of her loans was at 6.5% simple interest and the other at 7.2%. After one year, Stacey owed $ in interest. What was the amount of each loan?

9. Distance Problem D = R * T
D = Distance
R = Rate
T = Time
We have been comfortable with this arrangement, but in this section we will mix it up. We are going to see the rate being comprised of two components, one man made and one nature made.

10. Basic Distance Problem
Two cars leave Salt Lake City, traveling in opposite directions. One car travels at a speed of 80 km/h and the other at 96 km/h. In how many hours will they be 528 km apart?

11. Distance Problem
Given the picture, let us label the key parts.

12. Example
Cheri's motorboat took 3 hours to make a trip downstream with a 6mph current. The return trip against the same current took 5 hours. Find the speed of the boat in still water (no current).

13. Homework
Section 8.3
25, 26, 32, 35, 38, 45, 47, 50, 54, 74