Question 814183: Explain how you can tell(without graphing) whether a system of linear equations has one solution, no solutions, or infinitely many solutions. Be sure to account for linear equations that are not functions.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! put both equations in slope-intercept form: y = mx + b
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if the slopes are equal and the y-intercepts are equal, the equations describe the same line and the solution is infinitely many points.
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if the slopes are equal and the y-intercepts are not equal, the two lines do not intercept and have no points in common.
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if either equation is of the form: x = a
that equation describes a vertical line and its slope is undefined.
vertical lines intercept all non-vertical lines.
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if both lines are vertical and they are not the same line, the two lines do not intercept and have no points in common.
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otherwise, the lines intercept at exactly one point.
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
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Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
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