Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Classify a linear system as one solution, no solution, or infinitely many solutions
Problem
Classify the system \(y~=~2x~+~1\), \(y~=~-x~+~7\) as one solution, no solution, or infinitely many solutions.
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What this problem is really about
A system’s classification comes from how its two lines relate, not from their intercepts alone. We’ll read each slope and intercept from slope-intercept form, compare the slopes to distinguish crossing, parallel, and identical lines, and then equate the two output expressions as an algebraic check. The number of shared points determines the classification.
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