# 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 2nd equation from the 1st 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 linear 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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