Solving a linear system of linear equations in three variables by substitution the substitution method involves algebraic substitution of one equation into a variable of the other this will be the sample equation used through out the instructions equation 1 x 6y 2z 8 equation 2 x 5y 3z 2 equation 3 3x 2y 4z 18. Then you back solve for the first variable here is how it works ill use the same systems as were in a previous page solve the following system by substitution 2x 3y 2 4x y 24 the idea here is to solve one of the equations for one of the variables and plug this into the other equation. There are two basic ways to solve n equations with n unknowns substitution and elimination each of them can have variations for example matrix methods are extensions of the elimination method in this section we will explore substitution substitution method three variables and three unknowns let the variables be x y and z. Solving systems of equations using algebra calculator learn how to use the algebra calculator to solve systems of equations example problem solve the following system of equations x y7 x 2y11 algebra calculator will solve the system x y7 x 2y11 to get x3 and y4. Solving systems of equations by substitution method substitution is the most elementary of all the methods of solving systems of equations substitution method as the method indicates involves substituting something into the equations to make them much simpler to solve
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