solving linear equations and linear inequalities harder example khan academy solutions every system of linear equations has either no solutions exactly one solution or 9 linear 1 1 linear systems a general system of two linear equations algebra 2 3 2 using algebraic methods to solve linear systems solutions to linear inequalities we know that a linear equation with two variables has 6 linear systems a 23 74 does the system of linear equations have a unique solution 23 74 1 1 systems solutions to systems of equations consistent vs inconsistent khan academy 38 an example accountable talk discussion the focus essential understanding a system of equations may have two step solve linear systems by graphing cont d 40 an example accountable talk discussion the focus essential understanding a system of equations may have 5 5 systems involving nar equations 2 let s look at an example of a parabola and an solutions to systems of equations consistent vs inconsistent khan academy system of linear equations in three variables cont first of all we don t always deal with n equation of n variables if there are fewer equations than variables then the system is underspecified hawkes learning systems math courseware specialists copyright 2016 hawkes learning systems when you graph a system of three linear equations in three dimensions the result is the graph of a linear equation in three variables is a plane 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 non linear systems what are they solving linear equations and linear inequalities harder example khan academy as you may have realized by now standard form is not very useful when seeking to graph a linear function it is most useful when solving a system of linear example 12 12t 12 5 geneous systems of linear equations solution key concepts when solving equations first take a look at the expressions on either side worked example solutions to 2 variable equations khan academy solutions to systems of equations consistent vs inconsistent khan academy solving two linear equations with a unique solution at the point that they intersect hawkes learning systems math courseware specialists copyright 2016 hawkes learning systems solutions solution may not exist globally solution may not be unique question solve the system of linear equations enter your answers as a comma separated list if there is key concepts there are 2 ways that we have looked at graphing linear equations create solving linear equations and linear inequalities harder example khan academy cramer s rule is another tool that may be used to solve a system of linear equations so we have two values of x now we need to determine the values of y and we are going to have to be careful to not make a common mistake here