1. Day 2 – Solving Systems by Graphing

2. Example 1
Use substitution method to solve this system of equations. −𝑥+𝑦=4 3𝑥+𝑦=36

3. Answer
First solve −𝑥+𝑦=4 for 𝑦 to get 𝑦=𝑥+4. Then substitute 𝑥+4 for 𝑦 in the second equation, 3𝑥+𝑦=36.

4. Answer
Now substitute 8 for 𝑥 in the first equation, 𝑦=𝑥+4. So the solution is (8, 12). Always check your answers by substituting the x- and y- values into both of the original equations.

5. Example 2
In 1994, the whooping-crane population totaled 291. The number of captive whooping cranes was about the number of wild whooping cranes. How many whooping cranes were in captivity and how many were in the wild?

6. Whooping-crane population
Answer
Let c represent the number of whooping cranes living in captivity, and let w represent the number of whooping cranes living in the wild. First equation
Whooping-crane population
totaled
291
𝑐+𝑤 =

7. Answer
Second equation Since c is equal to 2 3 𝑤 in the second equation, substitute 2 3 𝑤 for 𝑐 in the first equation, 𝑐+𝑤=291.
Number of captive whooping cranes
was
𝟐 𝟑 the number of wild whooping cranes 𝑐 =
2 3 w

8. Answer

9. Substitute 175 for w In the second equation, 𝑐+𝑤=291.
Answer
Since 𝑤 represents the number of whooping cranes in the wild, and the number of these whooping cranes must be a whole number, round up to 175. So in 1994, there were 175 whooping cranes in the wild and 116 in captivity.
Substitute 175 for w
In the second
equation, 𝑐+𝑤=291.