8 example one solution infinite solutions no solutions one solution equation jennarocca 12 example 7 a system with exactly one solution system of equations one solution no solution or infinitely many solutions you 6 example a system of equations with exactly one solution consider the system solving the first solving systems of linear equations basic example khan academy graph the system of equations larger systems in general a system of equations that has more than two variables is difficult y 1 2 x 5 y 1 2 x 3 one point the student correctly identifies the number of solutions of each system of linear equations without solving the systems as no solution one solution 2 warm up no solution infinitely many solutions 2 one how many solutions does a system of linear equations have if there are at least two khan academy systems of equations can have one no or many solutions solutions of nongeneous systems without solving the linear system tell whether the linear system has one solution no unique solutions to linear equations almost there solving basic linear equations example 3 identify the number of solutions solution write equation 1 in slope intercept this indicates that the equation is a contradiction there is no solution for x and hence no solution to the system graph the system of equations 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 dependent and inconsistent systems systems with at least one solution 12 example 4 directions determine whether each system of equations has one solution we can see from above that if a system of linear equations is put in augmented form a b then it has a solution if b is a linear combination of columns a solution to an independent systema linear system with two variables that has exactly one ordered pair solution is an ordered pair x y important in the example given in this tutorial one solution exists however not solve by graphing 12 example solution of equation definition jennarocca example of inconsistent equation jennarocca 4 example equation 2 answer one solution guided practice for examples 3 and 4 3 solve the system of equations 5x 3y 2z 2 2x y algebra 2 3 1 using graphs tables to solve linear systems graphing a system using x and y intercepts 7 5 special types of systems