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Add the equations and eliminate the variable.Modify one equation so both equations have a variable that will cancel itself out when the equations are added together.Rewrite the equations so the variables line up.The elimination method follows these steps: Once the values for the remaining variables have been found successfully, they are substituted into the original equation in order to find the correct value for the other variable. The elimination method for solving systems of equations, also known as elimination by addition, is a way to eliminate one of the variables in the system in order to more simply evaluate the remaining variable. elimination method: Process of solving a system of equations by eliminating one variable in order to more simply solve for the remaining variable.

This is done by plugging both values into one or both of the original equations.

The steps of the elimination method are: (1) set the equations up so the variables line up, (2) modify one equation so both equations share a consistent variable that can be eliminated, (3) add the equations together to eliminate the variable, (4) solve, and (5) back-substitute to solve for the other variable.

Let's practice this by solving the following system of equations:

Solve this equation, and then back-substitute until the solution is found.

Continue until you have reduced the system to a single linear equation.

Substitute this expression into the remaining equations.

In the first equation, solve for one of the variables in terms of the others.

The substitution method consists of the following steps: When the resulting simplified equation has only one variable to work with, the equation becomes solvable. The substitution method for solving systems of equations is a way to simplify the system of equations by expressing one variable in terms of another, thus removing one variable from an equation.

substitution method: Method of solving a system of equations by putting the equation in terms of only one variable.

The solution to the system of equations can be written as an ordered pair ( x, y).

Do this by substituting the values you found back into the original equations.

It is very important to check your work once you have found a set of values for the variables.

The substitution method works by expressing one of the variables in terms of another, then substituting it back into the original equation and simplifying it.A system of equations is a set of equations that can be solved using a particular set of values.In a set of linear equations (such as in the image below), there is only one solution. This point is considered to be the solution of the system of equations. Shown graphically, a set of equations solved with only one set of answers will have only have one point of intersection, as shown below. Some systems have only one set of correct answers, while others have multiple sets that will satisfy all equations. Here, we will address the graphical method. The most common ways to solve a system of equations are: The graphical method: A way of visually finding a set of values that solves a system of equations.Ī system of equations (also known as simultaneous equations) is a set of equations with multiple variables, solved when the values of all variables simultaneously satisfy all of the equations.system of equations: A set of equations with multiple variables which can be solved using a specific set of values.To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.A system of linear equations will have one point of intersection, or one solution.There can be more than one solution to a system of equations.

To solve a system of equations graphically, graph the equations and identify the points of intersection as the solutions.