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Common Core Standard HSA-REI.C.5 Questions

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

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Grade 11 Matrices CCSS: HSA-REI.C.5
Which of the following is an equivalent system of equations to the one given?

[math]3x+5y=5[/math]
[math]2x+y=8[/math]
  1. [math]-7x = -35, \ \ 2x+y=8[/math]
  2. [math]3x+5y=5, \ \ -13x = -17 [/math]
  3. [math]3x+5y=5, \ \ 2x=8[/math]
  4. [math]y=11, \ \ 2x+y=8[/math]
Grade 10 Systems of Equations CCSS: HSA-REI.C.5
Which of the following systems of equations is equivalent to the one given? There may be more than one correct answer.
[math]4x+3y=-2[/math]
[math]2x-2y=6[/math]
  1. [math]4x+3y=-2, \ \ \ -7/2y = 7 [/math]
  2. [math]4x+3y=-2, \ \ \ 2x = -8[/math]
  3. [math]7y = -14, \ \ \ 2x-2y=6[/math]
  4. [math]x = -11, \ \ \ 2x- 2 = 6[/math]
Grade 10 Systems of Equations CCSS: HSA-REI.C.5
Which of the following systems of equations is equivalent to the one given? There may be more than one correct answer.
[math]2x+3y=6[/math]
[math]4x+2y=-4[/math]
  1. [math]3y=8, \ \ \ \ 4x+2y=-4[/math]
  2. [math]-2x=10, \ \ \ \ 4x+2y=-4[/math]
  3. [math]6x+5y=2, \ \ \ \ 4x+2y=-4[/math]
  4. [math]2x+3y=6, \ \ \ \ 4y=16[/math]

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