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 you need first
- Basic algebra
- Solving linear equations
- Understanding of what a solution to a system of equations means
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.
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