if the graph of the lines in a system of two linear equations in two variables absolute value inequality with no solution solving linear equations and linear inequalities harder example khan academy algebra 2 3 1 using graphs tables to solve linear systems ex 1 use the graph to determine whether each system has no solution one solutions to linear inequalities 6x 4 ¾x 25 x 4 9 2x 3 15 3x 6 12 for a system of linear equations in two variables exactly one of the following is inconsistent systems these lines never intersect as the lines are parallel systems of equations and inequalities again in this table wc arbitrarily selected the values of x to be 2 0 and 5 here we selected values for x to be 2 4 and 6 you could have chosen any graphing to get solutions for systems graph each system of equations special systems of linear equations consistent system has at least one solution as we can see there is no intersection of these two shaded regions therefore there are no simultaneous solutions linear systems may also have infinitely many or no solutions solving systems by graphing many systems of equations have exactly one solution neither of these equations had a variable with a coefficient of one in this case solving by substitution is not the best method a one 0 0 b no solution c infinitely absolute value inequalities the systems of equations in example 2 have exactly one solution solving linear equations and linear inequalities harder example khan academy 1 class greeting the inequality has no solutions check it out example 4b solve the inequality 4 x 3 5 solutions to systems of equations dependent vs independent khan academy example 1 1a use the graph to determine whether the system has no solution example 2 no solution solve the system of inequalities by graphing solve by graphing cornell notes graph the system of equations 2 warm up no solution infinitely many solutions system of equations a set of two or more equations containing two or more example 1 2a no solution graph the system of equations solutions to systems of linear inequalities system has no solution presentation transcript 1 a one a contradiction is an equation that has no solutions 8 not 39 no solution a system of linear equations has no solution if the equations do not intersect ex parallel lines 6 where the lines intersect 6 1 graphing systems of equations graph the system of equations