Justify elimination: replacing one equation in a two-variable system with a linear combination preserves solutions.
Find the first invalid step in an elimination solution
Problem
Audit these steps: \(1\)) \(2x~+~y~=~7\) and \(x~-~y~=~2\). \(2\)) Add the equations. \(3\)) \(3x~=~5\). \(4\)) \(x~=~5/3\). Identify the first invalid step and correct it.
Big Picture
What this problem is really about
Finding the first invalid step means auditing each transition in order, not merely noticing that the final value is wrong. We’ll verify that the equations were copied correctly, confirm the stated elimination operation, and recompute every variable column and the constants column. The earliest mismatch supplies the correction, and all later work must then be rebuilt from that corrected equation.
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