document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #490148 by TimothyLamb(4379)![]() ![]() You can put this solution on YOUR website! put both equations in slope-intercept form: y = mx + b \n" ); document.write( "--- \n" ); document.write( "if the slopes are equal and the y-intercepts are equal, the equations describe the same line and the solution is infinitely many points. \n" ); document.write( "--- \n" ); document.write( "if the slopes are equal and the y-intercepts are not equal, the two lines do not intercept and have no points in common. \n" ); document.write( "--- \n" ); document.write( "if either equation is of the form: x = a \n" ); document.write( "that equation describes a vertical line and its slope is undefined. \n" ); document.write( "vertical lines intercept all non-vertical lines. \n" ); document.write( "--- \n" ); document.write( "if both lines are vertical and they are not the same line, the two lines do not intercept and have no points in common. \n" ); document.write( "--- \n" ); document.write( "otherwise, the lines intercept at exactly one point. \n" ); document.write( "--- \n" ); document.write( "Solve and graph linear equations: \n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php \n" ); document.write( "--- \n" ); document.write( "Solve quadratic equations, quadratic formula: \n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php \n" ); document.write( "--- \n" ); document.write( "Convert fractions, decimals, and percents: \n" ); document.write( "https://sooeet.com/math/fraction-decimal-percent.php \n" ); document.write( "--- \n" ); document.write( "Calculate and graph the linear regression of any data set: \n" ); document.write( "https://sooeet.com/math/linear-regression.php \n" ); document.write( " |