Day 2 – Solving Systems by Graphing

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

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.

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.

Example 2 In 1994, the whooping-crane population totaled 291. The number of captive whooping cranes was about 2 3 the number of wild whooping cranes. How many whooping cranes were in captivity and how many were in the wild?

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 =

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

Answer

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 174 3 5 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.