Short Answer

Verifying Robotic Safety Boundaries

You are working as a quality control associate at an electronics assembly plant. A robotic solder arm's safety boundaries are modeled by the following system of linear equations:

3x+y=0{}3x + y = 0 x+2y=5x + 2y = -5

To ensure the robotic arm stays within safety zones, you must recall how to verify its coordinate pairs.

  1. State the algebraic rule for determining if any given coordinate pair (x, y) is a valid solution to a system of equations.
  2. Apply this rule to test the safety coordinate point (1,3)(1, -3) by showing your step-by-step substitution into both equations, and conclude whether or not it is a valid solution.

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Updated 2026-05-31

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