1. Solve the system of equations by substitution.
y = 3x − 10
3x + 2y = 16
2. Find the solution to the system of equations by substitution.
p = q + 2
2p + 3q = −26
3. Together, teammates Pedro and Ricky got 2,666 base hits last season. Pedro had 276 more hits than Ricky. How many hits did each player have?
4. River C is 100 miles longer than River D. If the sum of their lengths is 5,500 miles, what is the length of each river?
5. Writing A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 420 feet.
a. Determine the flag's length and width if the length is 110 feet greater than the width.
b. Write three situations to which you could apply the resulting system of equations.
6.
a. Reasoning Solve the system of linear equations using substitution.
x = 8y − 4
x + 8y = 6
b. Which expression would be easier to substitute into the other equation, in order to solve the problem? Explain your reasoning.
7. Error Analysis Tim incorrectly says that the solution of the system of equations is (−9, −4).
6g − 2h = −6
11 = h − 5g
a. What is the correct solution?
b. What error might Tim have made?
A. Tim made a mistake calculating the h-value.
B. Tim made a mistake calculating the g-value.
C. Tim switched the values of g and h.
D. Tim used opposite signs for g and h.
8. Swimming Pool On a certain hot summer day, 481 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $865.25. How many children and how many adults swam at the public pool that day?
9. Multiple Representations You are given the following system of equations.
2x − 5y = 26
x = 3y + 15
a. Find the solution of the system of equations by substitution.
b. Draw a picture using algebra tiles to show the substitution.
10. Multiple Representations
a. Find the solution of the system of equations by substitution.
3g − 11k = 17
2g = 4k + 8
b. Draw a picture using algebra tiles to show the substitution.
11. An airplane encountered a head wind during a flight between Joppetown and Jawsburgh, which took 4 hours and 42 minutes. The return flight took 4 hours. If the distance from Joppetown to Jawsburgh is 1,400 miles, find the airspeed of the plane (the speed of the plane in still air) and the speed of the wind, assuming both remain constant. Round speeds to the nearest tenth as needed.
12. Farmer Brown planted corn and wheat on his 370 acres of land. The cost of planting and harvesting corn (which includes seed, planting, fertilizer, machinery, labor, and other costs) is $280