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Solving by Graphing
Solving by Substitution
Solving by Elimination
Word Problems
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100
The solution to y = x + 4 y = 2x + 5
What is (-1,3)?
100
The solution to the system: x = 4y 2x + 3y = 22
What is (8,2)?
100
The solution to the system of equations: r + s = -6 r - s = -10
What is (-8,2)?
100
The sum of two numbers is 104. Their difference is 68. What are the numbers?
What are 86 and 18?
100
What does it mean to be a solution of a system of equations? (Two-part answer)
1) Ordered pair that satisfies BOTH equations 2) Point of intersection of two lines
200
The solution to y = 3x - 2 y = -x - 2
What is (0,-2)?
200
The solution to the system y = x - 2 3x - y = 16
What is (7,5)?
200
The solution to the system: 8a + 5b = 9 2a - 5b = -4
What is (0.5 , 1)?
200
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?
What is $30?
200
More than one equation to be solved at the same time is know as this.
What is a system of equations?
300
The solution to the system of equations: y = -3 x = 5
What is What is (5, -3)?
300
The solution to the system y = 3x - 1 - 6x + 2y = -2
What is infinitely many solutions?
300
The solution to 3x-10y=-25 4x+40y=20.
What is (-5,1)
300
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.00 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.
What is 400 advanced tickets, 200 game-day tickets?
300
What does it mean for a linear system to be consistent and independent?
There is one solution (and therefore one point of intersection).
400
The solution to the system of equations y = (1/3)x - 3 2x - y = 8
What is (3, -2)?
400
The solution to 4x+y=-2 -2x-3y=1
What is (-0.5, 0)
400
The solution to the system: 2x + 3y = 6 3x + 5y = 15
What is (-15, 12)?
400
The sum of Sally's age and her mother's age is 52. Sally's mother is 20 years older than Sally. This is the age of Sally's mother.
What is 36?
400
What does it mean for a system to be inconsistent?
There is no solution. The lines do not intersection and are parallel.
500
The solution to the system of equations: y - 3x = 3 y = 3x - 2
What is no solution?
500
The solution to x + 4y = 7 2y - 3x = 8.
What is (-9/7 , 29/14)
500
The solution to the system: (1/3)x + (1/4)y = 10 (1/3)x - (1/2)y = 4
What is (24,8)
500
The greater of two numbers is twice the lesser. If the greater is increased by 18, the result is 4 times the lesser. Find the greater number.
14
500
How can you tell whether a linear system is consistent & independent, consistent & dependent, or inconsistent WITHOUT solving? (3 part answer)
Look at the slope and y intercept: -If both are different, it is independent. -If the slopes are the same but the y intercept is different, the system is inconsistent. -If the slopes and y intercept are the same, the system is dependent.