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Elimination is the process of solving a systems of equations by eliminating one variable and solving for the other.
We can add two equations to eliminate one variable and solve for the other.
We can subtract two equations to eliminate one variable and solve for the other
Elimination Using Addition The coefficients of the y terms are additive inverses, we can eliminate the y variable by adding the two equations Example
Write the equations in column form and add The y term is eliminated Divide both sides by 4 Simplify
Now substitute 4 for x in either equation. In this case, we will Use the second equation as it is the easier equation. Second Equation Substitute x with 4 Subtract 4 from both sides Simplify The solution is (4, 1) You can check your work by substituting the solution into the first equation
Elimination using Subtraction Since the coefficients of the b terms are the same, we can eliminate the b -term by subtracting the two equations. Example
Write the equation in column form And subtract The variable b is eliminated Divide each side by -4 Simplify
Substitute c = -1 in either equation to find the value of b First equation Substitute -1 for c Simplify Add three on both sides Simplify Divide each side by 8 Reduce the fraction The solution is