A.REI.C.5: 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.

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.

Example Problems

What is the sum of all integer solutions to

1 < (x - 2)^2 < 25

?

Is the ordered pair

(2, 11)

a solution of the following equation?

y = 4x - 5

Is the ordered pair

(3, 11)

a solution of the following equation?

y = 4x + 1

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