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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
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.
x+2y+z=-4
x-y-z=-1
-5x+3y+4z=4
  1. (-1,-1,-1)
  2. (5,3,3)
  3. (3,-5,1)
  4. (-5,5,-9)
Grade 11 Systems of Equations CCSS: HSA-REI.C.7
At what point(s) do the following equations intersect?
y=2x+6
x2+(y+4)2=10
  1. (0,6)
  2. No intersection
  3. (1+5,4+25), (1-5,4-25)
  4. (4,-2), (9,-12)
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 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.
2x+2y+2z=18
3x+5y+4z=22
x+4y+2z=12
  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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