Starts With S
Solving by Graphing
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Solving by Elimination
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Solving by Substitution
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Word Problems
How many Solutions?
100
More than one equation to be solved at the same time is know as this.
Answer: System of Equations
100
The solution to the system of equations:
y = x + 4
y = 2x + 5
Answer: (-1,3)
100
The solution to the system of equations:
x + y = -6
x - y = -10
Answer: (-8,2)
100
The solution to the system:
x = 4y
2x + 3y = 22
Answer: (8, 2)
100
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
Answer: $30
100
How many solutions does the following system have?
y = 2x + 5
y = -2x + 5
Answer: 1 solution
The system has 1 solution because the slopes of the line are different.
200
The ratio of rise to run
Answer: slope
200
The solution to the system of equations:
y = 3x - 2
y = -x - 2
Answer: (0, -2)
200
The solution to the system:
8x + 5y = 9
2x - 5y = -4
Answer: (1/2, 1)
200
The solution to the system
y = x - 2
3x - y = 16
Answer: (7, 5)
200
Jenny wants to rent a truck for one day. She contacted two companies. Laguna’s Truck Rentals charges $20 plus $2 per mile. Salvatori’s Truck Rentals charges $3 per mile. After how many miles will the total cost for both companies be the same?
Answer: 20 miles
200
How many solutions does the system of equations have?
Answer: No solution
The system has no solution because the graph shows a pair of parallel line, therefore their is no point of intersection.
300
The answer to an equation or system of equations.
Answer: Solution or Solution Set
300
The solution to the system of equations:
y = -3
x = 5
Answer: (5, -3)
300
The solution to the system:
2x + 3y = 6
3x + 5y = 15
What is (-15, 12)?
300
The solution to the system
y = 3x - 1
7x + 2y = 37
Answer: (3, 8)
300
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
How many of each type of ticket was sold?
Answer: 400 advanced tickets, and 200 game-day tickets.
300
How many solutions are in the system of equations?
2x + 5y = 12
10y = 24 - 4x
Answer: Infinite solutions.
There are infinite solutions in the system because they are equivalent equations.
2x + 5y = 12 >>> 5y = 12 -2x
1/2(10y = 24 - 4x) >>> 5y = 12 - 2x
400
y = mx + b is more formally known as this.
Answer: slope-intercept form
400
The solution to the system of equations
y = (1/3)x - 3
2x - y = 8
Answer: (3, -2)
400
The solution to the system
2x - 4y = 12
-8x + 16y = -48
Answer: infinitely many solutions
400
The solution to the system
3s - 2t = 4
t = 2s - 1
Answer: (-2, -5)
400
The sum of two numbers is 104. Their difference is 68. What are the numbers?
Answer: 86 and 18
400
How many solutions does the system of equations have?
3x + 2y = 7
27x + 18y = 5
Answer: No solution
500
A method of solving systems by replacing one variable with an equivalent expression.
Answer: Substitution
500
The solution to the system of equations:
y - 3x = 3
y = 3x - 2
Answer: no solution
500
The solution to the system:
(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4
Answer: (24, 8)
500
The solution to the system
x + y = 12
x = (1/3)y
Answer: (3, 9)
500
Paul and Jacklyn are on a swim team.
- Paul has completed 140 laps so far this season. He completes an additional 12 laps during each practice.
- Jacklyn has completed 56 laps so far this season. She completes an additional 16 laps during each practice.
Paul and Jacklyn each attend the same number of practices. After how many more practices will Paul and Jacklyn have completed the same number of laps?
Answer: 21 practices
500
How many solutions does the system have?
Give an example of 2 lines that have 1 solution from the graph below:
Answer: Line A and Line B OR Line A and Line C
A system has one solution if the lines intersect at one point.