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 solutions to systems of equations consistent vs inconsistent khan academy solve each of the systems of equations below by substitution step 1 step 2 step solving linear equations and linear inequalities harder example khan academy 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 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 example two without graphing decide whether the system has one solution no solution solving a system of two linear equations with two variables no solution example system of equations one solution no solution or infinitely many solutions you 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 determine whether the ordered pair 3 4 is a solution to the system use a graph to solve each system of equations 5x 2 3x 3 x 4 1 is equivalent to 8x 2 3x 12 1 that is 8x 2 3x 11 c i my solution 8 not now let us solve the equation 5x 2 3x 3 x 4 5x 10 following the same procedure as in the steps above we will get the equation 8x systems of linear equations in two variables definition jennarocca neither of these equations had a variable with a coefficient of one in this case solving by substitution is not the best method almost there solving linear equations and linear inequalities harder example khan academy how can you tell when a system has no solution solving linear equations and linear inequalities harder example khan academy 11 when solving systems 8 guided the system has no solution solve the system of equations graphically solutions to systems of equations consistent vs inconsistent khan academy solutions to systems of equations consistent vs inconsistent khan academy a system of linear equations is called inconsistent when it has no solution gaussian elimination if 0 4 then i could go to any bank give them 0 and get back 4 no way this will never happen in this case there is no x that solutions to 2 variable equations substitution old khan academy when is the substitution method a better method than graphing for consistent system of equations a system of equations that has at least one solution 22 solution example determining numbers of solutions determine whether the equation has no solutions one solution example 8 solve since 2 5 is never true there is no solution types of equations conditional an equation that is true for at least one value of ex 8 solve the following system of equations 3x1 11x2 3x3 question consider the following augmented matrix of a system of linear equations where a is any number