solve systems of equations using elimination with addition and subtraction

solving systems of equations using elimination with addition and subtraction involves understanding and applying a method to find the solution to a system of two or more linear equations. The goal is to eliminate one variable at a time by adding or subtracting the equations in such a way that one of the variables cancels out, making it easier to solve for the remaining variable.

System of Equations: A set of two or more equations with the same set of variables.

What is Elimination Method?

As per the elimination method definition, it is about eliminating one of the terms containing any of the variables to make the calculations easier. This is done by multiplying or dividing a number by the equation(s) such that the coefficients of any one of the variable terms become the same. Then, we add or subtract both the equations to eliminate or remove that term from the result. That is why the elimination method is also called the addition method. For example, let us solve two linear equations containing two variables using the elimination method.

The elimination method is useful to solve linear equations containing two or three variables. We can solve three equations as well using this method. But it can only be applied to two equations at a time. Let us look at the steps

to solve a system of equations using the elimination method:

Step-1: The first step is to multiply or divide both the linear equations with a non-zero number to get a common coefficient of any one of the variables in both equations.

Step-2: Add or subtract both the equations such that the same terms will get eliminated.

Step-3: Simplify the result to get a final answer of the left out variable (let's say, y) such that we will only get an answer in the form of y=c, where c is any constant.

Step-4: At last, substitute this value in any of the given equations to find the value of the other given variable.

These are the elimination method steps to solve simultaneous linear equations.