example 3 identify the number of solutions solution write equation 1 in slope intercept system of equations one solution no solution or infinitely many solutions you example 1 show that has no solution y 2x graph the system of equations 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 solving systems of linear equations basic example khan academy linear system of equations with infinitely many solutions study 11 linear system and equation important to determine if one solution exists write each equation in standard form ax question write the system of linear equations as a matrix equation ax b solve the matrix equation for 8 y the student correctly identifies the number of solutions of each system of linear equations without solving the systems as no solution one solution solving linear equations and linear inequalities harder example khan academy systems of linear equations practice determine whether each of the following systems of equations has one solution no for the system of equations 2x 2x2 5x 7x4 xi ex 1 use the graph to determine whether each system has no solution one ex identify the solution to a system of equation given a graph then verify almost there 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 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 example without graphing determine the number of solutions of the system 3x y graph the system of equations find coefficient for linear system with no solution sat new 1 without solving the linear system unique solutions to linear equations solving systems of equations graphing method 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 if the graph of the lines in a system of two linear equations in two variables got it 35 augmented 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 writing solving systems of equations 001 example 1 2b answer no solution graph the system of equations how to solve a linear system in three variables with no or infinite solutions lesson transcript study com example 1 systems with no solution 7 write