Linear systems: graphs and number of solutions

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Learn it The solution of a linear system is the point where the lines cross. Different slopes: one solution. Same slope, different y-intercepts: parallel lines, no solution. Same line: infinitely many solutions.

Example: How many solutions: y = 2x + 3 and 4x − 2y = 8?

Second line: y = 2x − 4.
Same slope (2), different intercepts (3 and −4).
Parallel lines: no solution.

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