Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
2x - y = 7
2y = 4x - 14

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1 solution
infinite

Answer 1

\(\color{black}{2x - y = 7\quad \Longleftrightarrow \quad 2x - y \color{red}{-2x}= 7\color{red}{-2x}\quad \Longleftrightarrow \quad - y = 7-2x}\)
\((\color{black}{\quad \Longleftrightarrow \quad \color{red}{(-2)(}- y \color{red}{)}= \color{red}{(-2)(}7-2x\color{red}{)}\quad \Longleftrightarrow \quad 2y=-14+4x} \).

Answer 2

Can you tell me anything about the equations?\(\\[0.5em]\)
(How they relate, any differences/similarities?)

Answer 3

Your first equation: 2y = 4x - 14
Your second equation: 2y = -14 + 4x

Answer 4

Do you notice anything about the equations?