Answer:A Douglas Fir costs $27 and a Noble Fir costs $68.
Explanation:
To solve using elimination, follow these four steps:
Step 1: Make sure the equations have opposite x terms or opposite y terms.
Step 2: Add to eliminate one variable and solve for the other.
Step 3: Plug the result of Step 2 into one of the original equations and solve.
Step 4: State the solution.
solve
Before you can solve, you must write a system of equations. Let x represent the cost of a Douglas Fir tree, and let y represent the cost of a Noble Fir tree.
13x + 2y = 487
22x + 10y = 1,274
Now use elimination to solve the system of equations.
Step 1: Make sure the equations have opposite x terms or opposite y terms.
Currently, neither the x terms (13x and 22x) nor the y terms (2y and 10y) are opposites. Use multiplication to rewrite the equations with either opposite x terms or opposite y terms. One good approach is to multiply the first equation by –5.
–5(13x + 2y = 487)
→
–65x − 10y = –2,435
22x + 10y = 1,274
→
22x + 10y = 1,274
Now the y terms (–10y and 10y) are opposites.
Step 2: Add to eliminate one variable and solve for the other.
Add to eliminate the y terms, and then solve for x.
–65x − 10y = –2,435
+ ( 22x + 10y = 1,274 )
–43x + 0y = –1,161 Add to eliminate the y terms
–43x = –1,161 Simplify
x = 27 Divide both sides by –43
Step 3: Plug the result of Step 2 into one of the original equations and solve.
Take the result of Step 2, x = 27, and plug it into one of the original equations, such as 13x + 2y = 487. Then find the value of y.
13x + 2y = 487
13(27) + 2y = 487 Plug in x = 27
351 + 2y = 487 Multiply
2y = 136 Subtract 351 from both sides
y = 68 Divide both sides by 2
Step 4: State the solution.
Since x = 27 and y = 68, the solution is (27, 68).
A Douglas Fir costs $27 and a Noble Fir costs $68.