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Edmentum Integrated Math1 Unit4 Writing and Solving Systems Using Elimination
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00:00 Tutorial
26:32 Practice
53:27 Mastery Test
At the local market, Bill buys 3 juice boxes and 2 hot dogs at a cost of $8, while Sarah buys 2 juice boxes and 1 hot dog at a cost of $5.
The cost of each juice box is $ and the cost of each hot dog is $
The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches.
The admission fee for a charity event is $7 for children and $10 for adults. The event was attended by 700 people, and the total amount collected in admissions was $6,400.
Rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.
Mark is treating his family to ice cream. He buys 4 sundaes and 3 cones for a total of $26. Brian also buys ice cream for his family. His total is $29 for purchasing 2 cones and 5 sundaes.
Determine the system of equations that can be used to find the cost of one sundae, s, and the cost of one cone, c.
Classify each system of equations as having a single solution, no solution, or infinite solutions.
Roy and Elisa are buying tickets for the annual school concert. Roy buys 6 adult tickets and 2 child tickets for a total of $66. Elisa buys 5 adult tickets and 4 child tickets for a total of $62.
Determine the system of equations that can be used to find the cost of one adult ticket, a, and the cost of one child ticket, c
x − 2y = 15
2x + 4y = -18
x = 1, y = -6
x = 1, y = -7
x = 3, y = -6
x = 3, y = -7
William buys two bags of peaches and three bags of apricots for $17. Sylvia buys four bags of peaches and two bags of apricots for $22 from the same store. What is the cost of one bag of peaches?
What is the solution to this system of equations?
5x + 2y = 29
x + 4y = 13
x = 5, y = 3
x = 2, y = 5
x = 5, y = 2
x = 3, y = 2
System A System B System C
2x - 3y = 4 3x - 4y = 5 2x - 3y = 4
4x - y = 18 y = 5x + 3 12x - 3y = 54
Systems B and C have the same solution.
Systems A and C have the same solution.
Systems A and B have different solutions.
All three systems have different solutions.
System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three.
Which statement best describes the solution to this system of equations?
3x + y = 17
x + 2y = 49
It has no solution.
It has infinite solutions.
It has a single solution: x = 15, y = 17.
It has a single solution: x = -3, y = 26.
An office supply company orders packs of pens for two of its stores. For the first store, the order is for 60 packs of ballpoint pens and 25 packs of gel pens, for a total of $355. For the second store, the order is for 120 packs of ballpoint pens and 30 packs of gel pens, for a total of $570.
Create and solve a system of equations to determine the cost of one pack of ballpoint pens and one pack of gel pens.
The cost of one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $7.
The cost of one pack of ballpoint pens is $4 and the cost of one pack of gel pens is $3.
The cost of one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $4.
The second equation in system B is -7x = 14. The solution to system B will not be the same as the solution to system A.
The second equation in system B is 7x = 30. The solution to system B will be the same as the solution to system A.
The second equation in system B is 7x = 30. The solution to system B will not be the same as the solution to system A.
When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.
When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.
When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.
When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.
A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon.
How many yards are on one roll of lace ribbon and one roll of satin ribbon?
A test is worth a total of 150 points and contains 70 questions. Some of the questions are worth 2 points, and some are worth 4 points.
The first equation in the system of equations that models this situation is x + y = 70, where x represents the number of 2-point questions and y represents the number of 4-point questions
26:32 Practice
53:27 Mastery Test
At the local market, Bill buys 3 juice boxes and 2 hot dogs at a cost of $8, while Sarah buys 2 juice boxes and 1 hot dog at a cost of $5.
The cost of each juice box is $ and the cost of each hot dog is $
The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches.
The admission fee for a charity event is $7 for children and $10 for adults. The event was attended by 700 people, and the total amount collected in admissions was $6,400.
Rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.
Mark is treating his family to ice cream. He buys 4 sundaes and 3 cones for a total of $26. Brian also buys ice cream for his family. His total is $29 for purchasing 2 cones and 5 sundaes.
Determine the system of equations that can be used to find the cost of one sundae, s, and the cost of one cone, c.
Classify each system of equations as having a single solution, no solution, or infinite solutions.
Roy and Elisa are buying tickets for the annual school concert. Roy buys 6 adult tickets and 2 child tickets for a total of $66. Elisa buys 5 adult tickets and 4 child tickets for a total of $62.
Determine the system of equations that can be used to find the cost of one adult ticket, a, and the cost of one child ticket, c
x − 2y = 15
2x + 4y = -18
x = 1, y = -6
x = 1, y = -7
x = 3, y = -6
x = 3, y = -7
William buys two bags of peaches and three bags of apricots for $17. Sylvia buys four bags of peaches and two bags of apricots for $22 from the same store. What is the cost of one bag of peaches?
What is the solution to this system of equations?
5x + 2y = 29
x + 4y = 13
x = 5, y = 3
x = 2, y = 5
x = 5, y = 2
x = 3, y = 2
System A System B System C
2x - 3y = 4 3x - 4y = 5 2x - 3y = 4
4x - y = 18 y = 5x + 3 12x - 3y = 54
Systems B and C have the same solution.
Systems A and C have the same solution.
Systems A and B have different solutions.
All three systems have different solutions.
System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three.
Which statement best describes the solution to this system of equations?
3x + y = 17
x + 2y = 49
It has no solution.
It has infinite solutions.
It has a single solution: x = 15, y = 17.
It has a single solution: x = -3, y = 26.
An office supply company orders packs of pens for two of its stores. For the first store, the order is for 60 packs of ballpoint pens and 25 packs of gel pens, for a total of $355. For the second store, the order is for 120 packs of ballpoint pens and 30 packs of gel pens, for a total of $570.
Create and solve a system of equations to determine the cost of one pack of ballpoint pens and one pack of gel pens.
The cost of one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $7.
The cost of one pack of ballpoint pens is $4 and the cost of one pack of gel pens is $3.
The cost of one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $4.
The second equation in system B is -7x = 14. The solution to system B will not be the same as the solution to system A.
The second equation in system B is 7x = 30. The solution to system B will be the same as the solution to system A.
The second equation in system B is 7x = 30. The solution to system B will not be the same as the solution to system A.
When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.
When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.
When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.
When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.
A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon.
How many yards are on one roll of lace ribbon and one roll of satin ribbon?
A test is worth a total of 150 points and contains 70 questions. Some of the questions are worth 2 points, and some are worth 4 points.
The first equation in the system of equations that models this situation is x + y = 70, where x represents the number of 2-point questions and y represents the number of 4-point questions
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