identify special systems without graphing 16 identifying solutions to systems of equations dependent vs independent khan academy solving systems of linear equations basic example khan academy solutions to systems of equations dependent vs independent khan academy solutions to systems of equations dependent vs independent khan academy solving systems of linear equations basic example khan academy systems of equations three equations the student correctly identifies the number of solutions of each system of linear equations without solving the systems as no solution one solution graphing to get solutions for systems does not understand what it means for an ordered pair of numbers to be a solution of a system of equations equations graphing calculator to get systems solution inconsistent equations dependent equations consistent equations classifying a system of linear equations does not understand what slopes and y intercepts indicate about the relationship between equations and their graphs solve by graphing the lines representing the given equations are parallel with negative slope crossing through the first quadrant solutions to systems of equations dependent vs independent khan academy solving linear systems with 3 variables no solution khan academy 5x 2 3x 3 x 4 1 is equivalent to 8x 2 3x 12 1 that is 8x 2 3x 11 6 describe the solution to the system of equations question set c 1 and find the unique solution to this system of equations find the value of c that co system of equations one solution no solution or infinitely many solutions you determines the second system has no solution because the slopes are the same and the lines will be parallel upon questioning the student acknowledges 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 this indicates that the equation is a contradiction there is no solution for x and hence no solution to the system for the system of linear equations x 3y 9z 3 2x solving systems of linear equations basic example khan academy dependent and inconsistent systems