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Common Core Standard HSA-REI.C.6 Questions

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

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Grade 11 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
Kevin weighs sets of small rock samples for his science class. A set of 2 quartz, 2 mica, and 1 granite rocks weigh 22 grams. A set of 1 quartz, 1 mica, and 2 granite rocks weigh 20 grams. A set of 1 quartz, 3 mica, and 1 granite rocks weigh 20 grams. Samples of each rock type have the same weight. Write a system of linear equations. Solve the system to determine the weight of each rock. x = weight on the quartz rock, y = the weight of the mica rock, and z = the weight of the granite rock.
  1. [math]x + y + z = 22, \ \ \ 2x + 2y + 2z = 20, \ \ \ 2x + y + z = 20; \ \ \ (x,y,z) = (6, 5,3)[/math]
  2. [math]2x+y+2z=22, \ \ \ x+2y+2z=20, \ \ \ x+2y+z+20; \ \ \ (x,y,z) = (5,6,3)[/math]
  3. [math]2x+2y+z=22, \ \ \ x+y+2x=20, \ \ \ x+3y+z=20; \ \ \ (x,y,z) = (5,3,6)[/math]
  4. [math]x+y+2z=22, \ \ \ 2x+z+2z=20, \ \ \ x+2y+2z=20; \ \ \ (x,y,z) = (3,6,5)[/math]
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
Solve the system of equations.

[math]2x-y+2z=15[/math]
[math]-x+y+z=3[/math]
[math]3x-y+2z=18[/math]
  1. [math](5,3,1)[/math]
  2. [math](3,1,5)[/math]
  3. [math](-3,5,1)[/math]
  4. [math]"No Solution"[/math]
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
3x - 2y = 7
x + 3y = 6
  1. x = 3, y = 1
  2. x = -1, y = 1.67
  3. x = 0, y = 1
  4. x = 3, y = -2
Grade 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
The manager of the White Hall Spartan Movie Theatre found that Saturday's sales were $3,675. He knew that a total of 650 tickets were sold Saturday. Adult tickets cost $7.50, and children's tickets cost $4.50. How many of each kind of ticket were sold?
  1. Children: 250 tickets; Adults: 400 tickets
  2. Children: 160 tickets; Adults: 490 tickets
  3. Children: 344 tickets; Adults: 306 tickets
  4. Children: 400 tickets; Adults: 250 tickets
Grade 9 Systems of Equations CCSS: HSA-REI.C.6
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