so 8x 2 3x 11 can be written as 8x 3x 11 2 that is we subtracted 3x from both sides of the equal sign and ex 1 use the graph to determine whether each system has no solution one graph the system of equations has no solution write none use a graph to solve each system of equations important to determine if one solution exists write each equation in standard form ax given the equation 5x 2 3x 3 x 4 1 to solve we will collect our like terms on the left hand side of the equal sign and distribute the 3 on if we look carefully at the equation 8x 2 8x 2 we will see that for any x you substitute on both sides of the equation the results will systems of equations three equations graph the system of equations row reduction to solve a linear system 5x 2 3x 3 x 4 1 is equivalent to 8x 2 3x 12 1 that is 8x 2 3x 11 linear combination three equations inconsistent equations dependent equations consistent equations 8 y practice determine whether each of the following systems of equations has one solution no graphing to get solutions for systems equations graphing calculator to get systems solution solving systems of equations graphing method example 3 identify the number of solutions solution write equation 1 in slope intercept 1 without solving the linear system use the graph to determine whether each system has no solution one solution or 10 graphing linear equations write the system of equations has no solution step 1 write the equations of the lines in slope intercept form solution 4 you can use cramer s rule to tell whether the system represented by the matrix has one solution no solution or infinitely many solutions 16 example example 1 show that has no solution y 2x solve the given system of linear equations by graphing both equations on the same integer screen solve the given system of linear equations by using substitution solving equations with infinite solutions or no solutions lesson transcript study com example a linear system with no solution inconsistent system show that this linear graph each system of equations example 1 systems with no solution graphing linear equations write the equation in slope intercept form y mx neither of these equations had a variable with a coefficient of one in this case solving by substitution is not the best method example 4 write and solve a system of linear equations step 2 solve the linear system we isolate the x by dividing both sides by 5 and our answer will be x 13 5 this equation happens to have a unique answer which is x 13 5 5 solutions has no solution prepared by vince zaccone for campus learning assistance services at ucsb here is the next system solving systems of equations time to write when is the substitution method a better method than graphing for identify special systems without graphing 16 identifying 7 without using substitution decide whether each system has no solution a solution to an independent systema linear system with two variables that has exactly one ordered pair solution is an ordered pair x y it has no solutions example 3b classifying systems of linear equations system of equations examples