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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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Which of the following is an equivalent system of equations to the one given?

$3x+5y=5$
$2x+y=8$
1. $-7x = -35, \ \ 2x+y=8$
2. $3x+5y=5, \ \ -13x = -17$
3. $3x+5y=5, \ \ 2x=8$
4. $y=11, \ \ 2x+y=8$
Grade 11 Systems of Equations CCSS: HSA-REI.C.5
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.
$4x+3y=-2$
$2x-2y=6$
1. $4x+3y=-2, \ \ \ -7/2y = 7$
2. $4x+3y=-2, \ \ \ 2x = -8$
3. $7y = -14, \ \ \ 2x-2y=6$
4. $x = -11, \ \ \ 2x- 2 = 6$
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.
$2x+3y=6$
$4x+2y=-4$
1. $3y=8, \ \ \ \ 4x+2y=-4$
2. $-2x=10, \ \ \ \ 4x+2y=-4$
3. $6x+5y=2, \ \ \ \ 4x+2y=-4$
4. $2x+3y=6, \ \ \ \ 4y=16$
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