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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 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
Grade 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
Grade 10 Area CCSS: HSA-CED.A.3, HSA-REI.C.6
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. $x + y + z = 22, \ \ \ 2x + 2y + 2z = 20, \ \ \ 2x + y + z = 20; \ \ \ (x,y,z) = (6, 5,3)$
2. $2x+y+2z=22, \ \ \ x+2y+2z=20, \ \ \ x+2y+z+20; \ \ \ (x,y,z) = (5,6,3)$
3. $2x+2y+z=22, \ \ \ x+y+2x=20, \ \ \ x+3y+z=20; \ \ \ (x,y,z) = (5,3,6)$
4. $x+y+2z=22, \ \ \ 2x+z+2z=20, \ \ \ x+2y+2z=20; \ \ \ (x,y,z) = (3,6,5)$
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.

$2x-y+2z=15$
$-x+y+z=3$
$3x-y+2z=18$
1. $(5,3,1)$
2. $(3,1,5)$
3. $(-3,5,1)$
4. $"No Solution"$
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
Grade 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
Grade 9 Systems of Equations CCSS: HSA-REI.C.6
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-REI.C.6
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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