Vault Of Euclid

Solving an Inconsistent System of Two Linear Equations

Systems of linear equations warmup

(a) Solve the system \begin{align*} L_1&: x - 3y = 4 \\ L_2&: -2x + 6y = 5 \end{align*}
linear-systemselimination-methodno-solutiondegenerate-equationparallel-linesinconsistent-systemlinear-algebratwo-variablessystems-of-equations

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What this problem tests

Tests the student's ability to apply the elimination method and correctly interpret a degenerate equation as indicating an inconsistent system.

This is a fundamental problem in introductory linear algebra and algebra courses, demonstrating what happens algebraically when a system has no solution.