Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
The last six problems model real situations as systems (A-CED.A.3): tickets, mixtures, plans, boats, coins and a garden. Check every ordered pair in both equations.
Standards: A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3 · Level: Grade 9 Algebra 1
Problem 1 Check a solution ★★★
Is (3, 1) a solution of the system x + y = 4 and 2x − y = 5?
Problem 2 Check a failing pair ★★★
Is (2, −1) a solution of y = 3x − 7 and x + 2y = 1?
Problem 3 Substitution with y = 2x ★★★
Solve by substitution: y = 3x and x + y = 28.
Problem 4 Substitution with x = y + 4 ★★★
Solve by substitution: x = y + 4 and 2x + y = 17.
Problem 5 Read the graph ★★★
Two lines are drawn below. State the coordinates of the point they share.
Problem 6 Elimination by adding ★★★
Solve by elimination: x + y = 15 and x − y = 5.
Problem 7 Elimination with opposite terms ★★★
Solve by elimination: 7x + 3y = 27 and 4x − 3y = 6.
Problem 8 Scale one equation ★★★
Solve: 2x + 5y = 26 and 3x − y = 5.
Problem 9 Scale both equations ★★★
Solve: 4x + 3y = 25 and 3x − 2y = 6.
Problem 10 No solution ★★★
Solve 2x + 4y = 14 and 2x + 4y = 8, and explain the result with the graph.
Problem 11 Infinitely many solutions ★★★
Solve 10x − 4y = 14 and 5x − 2y = 7.
Problem 12 Why elimination works ★★★
Replace the second equation of x + y = 9, 2x + 5y = 33 by (second) − 2·(first). Show that the new system has the same solution.
Problem 13 Solve by graphing ★★★
Solve by graphing y = 2x − 1 and y = −x + 8.
Problem 14 Two functions equal ★★★
Find the value of x where f(x) = 4x − 7 equals g(x) = −x + 13, and the common output.
Problem 15 Ticket sales ★★★
A school play sold 480 tickets. Adult tickets cost $12 and student tickets cost $7. The total was $4,530. How many of each kind were sold?
Problem 16 Coffee mixture ★★★
A shop mixes $8-per-pound beans with $14-per-pound beans to make 10 pounds that cost $10.40 per pound. How many pounds of each?
Problem 17 Phone plans ★★★
Plan A costs $24 plus $0.08 per minute. Plan B costs $9 plus $0.18 per minute. At what usage are the two bills equal, and what is that bill? Use the graph.
Problem 18 Kayak and river ★★★
A kayaker paddles 18 miles with the river current in 2 hours, then 18 miles back against it in 3 hours. How fast does the kayaker paddle in still water, and how fast does the river flow?
Problem 19 Nickels and dimes ★★★
A jar has 35 coins, all nickels and dimes, worth $2.80. How many of each coin?
Problem 20 Garden dimensions ★★★
The length of a rectangular garden is 3 feet more than twice its width, and its perimeter is 66 feet. Find both dimensions.
