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Lin Alg Question: System 1: {2x1+3x2=4, 5x1+6x2=7)}, system 2: {λ2x1+λ3x2=λ4, 5x1+6x2=7} (λ is non zero and...

Lin Alg Question:

System 1: {2x1+3x2=4, 5x1+6x2=7)}, system 2: {λ2x1+λ3x2=λ4, 5x1+6x2=7} (λ is non zero and λ is all real numbers)

How can we prove that all solutions of system 1 are also solutions of system 2, and how can we prove that all solutions fo system 2 are solutions to system 1?

If I have 2 linear equations and one equation is just a scalar multiple of the other, then are these 2 equations the same?

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