You got the system of two linear equations in two unknowns. Įxample 3Solve the system of linear equations Now, back-substitute the found values and into the first equation of the system (3):Īnswer. You don't need to make more calculations! You are lucky! You got the system whose solution is obvious: and. You will get the system of two equations in two unknowns and Substitute it into the second and the third equations. Įxample 2Solve the system of linear equations The check shows that the solution is correct.Īnswer. = for the left side of the third equation, and it is identical to its right side. = for the left side of the second equation, and it is identical to its right side = for the left side of the first equation, and it is identical to its right side Simply substitute the found values of, and into the original equations. Thus the solution of the original system of equations is,. Now, back-substitute the found values and into the first equation of the system (1): Back-substitute it into either equation of the intermediate system (2), for example, into the first one. Simplify it by opening parentheses and collecting common terms. So, let us express from the first equation of the system (2)Īnd substitute it into the second equation. But this time I will use the same substitution method to stay in frame of this method. In this way you immediately get the solution of the system (2). Perhaps, the simplest way to solve it is to apply the Elimination method (see the lesson Solution of the linear system of two equations in two unknowns by the Elimination method in this site) by distracting the first equation from the second one. Simplify these two equations to the standard form by collecting common terms:

Substitute it into the first and the second equations. As the last step, back-substitute the two found values for unknowns into either appropriate of the original equations - it will allow you to find the last unknown.Įxamples below show how this method works.Įxample 1Solve the system of linear equations Then back-substitute the found value into the intermediate system of two linear equations in two unknowns to get the second unknown. For it, you express the second unknown via the third one using one of the two linear equations of the obtained system, and then substitute it into the remaining equation of this system.Īfter completing this, you will get the single linear equation in one unknown which you can easily solve. When this step is done, you solve the obtained system of two linear equations by repeatedly applying the substitution method as described in the lesson Solution of the linear system of two equations in two unknowns by the Substitution method of the section Algebra-I in this site. In this step you reduce the original system of three linear equations in three unknowns to the system of two linear equations in two unknowns. The method is to express one variable via two others using one equation and then to substitute this expression into the two remaining equations.

In this lesson you will learn the Substitution method for solving systems of three linear equations in three unknowns. Solving systems of linear equations in 3 unknowns by the Substitution method

Steps for 3 equation systems