solutions to systems of equations dependent vs independent khan academy solutions to systems of equations dependent vs independent khan academy solutions to systems of equations dependent vs independent khan academy solving systems of linear equations basic example khan academy 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 graphing to get solutions for systems the lines representing the given equations are parallel with negative slope crossing through the first quadrant 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 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 neither of these equations had a variable with a coefficient of one in this case solving by substitution is not the best method 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 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 the figure depicts an xy plane with two linear lines intersecting at the point 1 2 5x 2 3x 3 x 4 1 is equivalent to 8x 2 3x 12 1 that is 8x 2 3x 11 solving linear systems with 3 variables no solution khan academy dependent system of linear equations examples lesson transcript study com solutions to systems of equations dependent vs independent khan academy how to solve a linear system in three variables with no or infinite solutions lesson transcript study com solution systems of equations with elimination 3y 4x 11 y 2x 13 khan academy 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 let s graph the equations to see if the intersection point is indeed 3 1 clearing fractions and decimals given a linear system where the equations have 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 solve by graphing applying systems of linear equations to market equilibrium steps example find the solution to a system of linear equations by looking at their graphs learnzillion back substitution your graph will look like this solving a system of equations with two unknowns solutions to systems of equations dependent vs independent khan academy weight of coffee graph is teacher made how to solve linear systems using gaussian elimination lesson transcript study com