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You're a manager in a company that produces rocket ships. Machine $A$ and Machine $B$ both produce cockpits and propulsion systems. Machine $A$ ran for $22$ hours and produced $3$ cockpits and $5$ propulsion systems. Machine $B$ ran for $44$ hours and produced $6$ cockpits and $10$ propulsion systems.$\newline$Assume both machines produce cockpits at the same rate and both produce propulsion systems at the same rate.$\newline$Can we use a system of linear equations in two variables to solve for a unique amount of time that it takes each machine to produce a cockpit and to produce a propulsion system?$\newline$Choose $1$ answer:$\newline$(A) Yes; it takes Machine $A$ and Machine $B$ $2$ hours to produce a cockpit and $4$ hours to produce a propulsion system.$\newline$(B) Yes; it takes Machine $A$ and Machine $B$ $4$ hours to produce a cockpit and $2$ hours to produce a propulsion system.$\newline$(C) No; the system has many solutions.$\newline$(D) No; the system has no solution.