2 3 a system of linear equations consists of two or more linear equations made up of two or more variables that all equations in the system are considered simultanious such we can see the solution to a system of two linear equations clearly by plotting the graph of each equation there are three variables types of systems of each having a different two linear equations type of in two solution an independent system has exactly one solution the coordinate pair intersect is the only solution x y the point where the two lines an inconsistent system has no solution the two lines are parallel and will never intersect a dependent system has infinitely many solutions the lines are the same Class work a 2 3 1713 4 y 41kx 121K m m 4 3 K can be any real except 6 K 6 b K 6 b I bz no solutions when K 6 ex 3 15 20 5 y y 3 4 12 4 3 4 50 12 12 16 50 no solution inconsistent system ex 4 144 4 30 10g 104 30 30 30 X 3 54 186513 5919 infinitely many solutions dependent 2 3 cont system to of system inconsistent when solving a system of two linear equations in two unknowns graphically we graph both equations and look for intersection point s one exists the if in inconsistent or determine dependent cases we the existence of a can still graph the solution and type if the system is parallel it has no solution and is if the two lines are identical the system has infinitely many solutions and is a dependent system class notes 2 3 6 6 124 25 24 9 49 7 44 18 X 3