![]() ![]() This means that when you have the equations lined up by column and variable, as in the example above, you want the sum of the column of a variable to equal 0. ![]() The goal of elimination is to cancel out a variable. When using the elimination method, try to think of the system of equations as one big addition column, except that there is no carrying, and you can only add and subtract corresponding variables and constants. This organizes the systems of equations by aligning each term in one equation with their corresponding term in the other. Before starting, it is very important that both equations are in the standard form Ax + By = C. To solve systems of equations using the elimination method, you need to eliminate one variable. If both equations return true statements, as shown below, then you have successfully used the subtitution method! x = 10 ![]() You can check your answers by plugging the x- and y-values into the original equations and simplifying. Now you have the values of both coordinates! The solution to the system of equations is (10, 1). To solve for the remaining variable, you can plug in the value of the variable you just solved for into either of the original equations. Now, because there is only one variable left in the equation, you can solve for that variable! Next, substitute the equivalent of the variable you just solved for into the corresponding variable in the other equation. ![]()
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