# Study of substitution method and its definition

As discussed above, the **substitution method** will be used when you have a system of equations. Systems which require **solving by substitution method** usually have 2 or more variables.

The **substitution method definition** is very simple: You have to find the solution of a system of equations. In order to make use of the **algebra substitution method**, write one of your equation in terms of x and y and then substitute the result of the variable into the other equation. Using this **substitution method for solving equations**, you will remain with only one equation with a single variable which is very easy to solve.

## Some important substitution method examples

Now that you theoretically know the **method of substitution**, it's time to take some **substitution method examples ** so that you can fully understand the principle.

In the first **substitution method example,** we will take two equations with two variables and try to** solve by the substitution method. **The equations are 43x + 31y = 241 & 31x + 43y = 277.

Adding the equations, we get 74x + 74y = 518. Now dividing it by 74, x + y = 7 --(i)

Now subtracting the 2^{nd} equation from the 1^{st} one, i.e. 12x - 12y = -36, simplifying it gives x - y = -3 –(ii). Adding (i) and (ii) expressions, we obtain x = 2, y = 5. Therefore, we solved the exercise by **system of equations substitution method** and we found the solution x = 2 and y = 5.

** **Now we'll see the **l**inear equations** **and **solve by substitution method. **The **substitution method problems** help to improve our mathematical skills and represent practical examples of how the exercises should be solved. Next, we will solve 2 **substitution method linear equations**.

A system of linear equations is a combination of two linear equations in two variables. In this example, we convert two equations having two variables into a single one. Let us solve the system of equations by substitution method** **2x + 5y + 11 = 0 and y - 3x + 9 = 0. This equations can also be written as 2x + 5y = -11 --(i) and y - 3x = -9 --(ii). Solving (ii) for y, y = 3x - 9 ... (iii) Substituting the value of y in (i), 2x + 5(-9 + 3x) = -11 => 2x - 45 + 15x = -11 => 17x - 45 = -11 => 17x = -11 + 45 => 17x = 34 => x = 2. Once we have x, it's simple to find y, y = 3*2 - 9 = -3.

Thus we have seen that **substitution method algebra** is a simple and efficient method used for solving systems of equations.

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