Substitution Worksheet With Answer Key - Waynesville R-Vi School District Page 19
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386-2 Substitution
This equation is an identity. So, there are infinitely many solutions.
In 2000, the demand for nurses was 2,000,000, while the supply was only 1,890,000. The projected
demand for nurses in 2020 is 2,810,414, while the supply is only projected to be 2,001,998.
a. Define the variables, and write equations to represent these situations.
b. Use substitution to determine during which year the supply of nurses was equal to the demand.
a. Let x = number of years since 2000, and let y = the number of nurses. Find the slope for the supply and the
demand.
Next, write an equation for each relationship.
An equation for the supply is y = 5599.9x + 1,890,000 and an equation for the demand is y = 40,520.7x + 2,000,000.
5599.9
b. y =
x + 1,890,000
y = 40,520.7x + 2,000,000
Substitute 5599.9x + 1,890,000 in for y into the second equation.
Since x
equal to the demand for nurses was during 1996.
The table shows the approximate number of tourists in two areas of the world during a
recent year and the average rates of change in tourism.
Page 19
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