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Eleventh Grade (Grade 11) Systems of Equations Questions

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Grade 11 Systems of Equations CCSS: HSA-REI.C.6
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
What is the solution to the following system?

[math]{:(x+2y+3z = ,-5),(3x+y-3z = , 4),(-3x+4y+7z = , -7):}[/math]
  1. [math](-1,0,-2)[/math]
  2. [math](1,1,2)[/math]
  3. [math](-1,1,-2)[/math]
  4. [math](0,1,2)[/math]
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
Solve.
[math] x + 2y + z = -4 [/math]
[math] x - y - z = -1 [/math]
[math] -5x + 3y + 4z = 4 [/math]
  1. [math](-1,-1,-1)[/math]
  2. [math](5,3,3)[/math]
  3. [math](3,-5,1)[/math]
  4. [math](-5, 5, -9)[/math]
Grade 11 Systems of Equations CCSS: HSA-REI.C.7
At what point(s) do the following equations intersect?
[math]y=2x+6[/math]
[math]x^2+(y+4)^2=10[/math]
  1. [math](0,6)[/math]
  2. No intersection
  3. [math](1+sqrt(5), 4+2sqrt(5)), \ (1-sqrt(5), 4-2sqrt(5))[/math]
  4. [math](4,-2), \ (9,-12)[/math]
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 11 Systems of Equations
Which of the following is the correct definition of equivalent systems?
  1. A number's distance from zero on the number line.
  2. An inequality in two variables whose graph is a region of the half plane.
  3. A set of two or more equations that use the same variables.
  4. Systems that have the same solutions.
Grade 11 Systems of Equations CCSS: HSA-REI.C.6
Solve.
[math]2x + 2y + 2z = 18[/math]
[math]3x + 5y + 4z = 22[/math]
[math]x + 4y + 2z = 12[/math]
  1. x = 38, y = 16, z = -37
  2. x = 12, y = 8, z = -11
  3. x = 22, y = 8, z = -21
  4. x = -20, y = -8, z =-21
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