Question

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Part 1
Space Exploration  Two rovers are exploring a planet. The system of equations below shows each​ rover's elevation y at time x. Without graphing these​ equations, what conclusion can you make about the system of​ equations? Use pencil and paper. Interpret your result in the context of the problem.
Rover A:
yequals
1.3xminus2
Rover B:
7yequals
9.1xminus14
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Part 1
What conclusion can you make about the system of​ equations?
A.
The system has no solution.
B.
The system has infinitely many solutions.
C.
The system has exactly one solution.

Answer 1

B. The system has infinitely many solutions.

Reason: Multiply Rover A's equation by 7: 7y = 7(1.3x − 2) = 9.1x − 14, which is exactly Rover B's equation. The two equations represent the same line (same slope and same intercept), so every (x,y) on that line is a solution. In context, the rovers have the same elevation at every time x.