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For example, if a = –6 and b = 5, then both equations are made true. In fact, any a and b replacement that makes one of the equations true, also makes the other equation true. When this occurs, the system of equations does not have a unique solution. Now if you were to subtract one equation from the other, the result is 0 = 0. To check the solution, replace each x in each equation with 5 and replace each y in each equation with 3.

Of course, if the number in front of a letter is already the same in each equation, you do not have to change either equation. Insert x = 5 in one of the original equations to solve for y. The equations can be subtracted, eliminating the y terms. Now the y is preceded by a 3 in each equation. You need to be aware of these when you use the addition/subtraction method.įirst multiply the bottom equation by 3. In some situations you do not get unique answers or you get no answers. In Example and Example, a unique answer existed for x and y that made each sentence true at the same time. Now inserting 5 for x in the first equation gives the following:īy replacing each x with a 5 and each y with a 2 in the original equations, you can see that each equation will be made true. Solve for the other unknown by inserting the value of the unknown found in one of the original equations.Īdding the equations eliminates the y‐terms.Add or subtract the two equations to eliminate one letter.Multiply one or both equations by some number(s) to make the number in front of one of the letters (unknowns) the same or exactly the opposite in each equation.To use the addition/subtraction method, do the following:

This method is also known as the elimination method. There are three common methods for solving: addition/subtraction, substitution, and graphing. If you have two different equations with the same two unknowns in each, you can solve for both unknowns. Solving Systems of Equations (Simultaneous Equations) Quiz: Linear Inequalities and Half-Planes.Solving Equations Containing Absolute Value.Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Quiz: Solving Systems of Equations (Simultaneous Equations).Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Quiz: Simplifying Fractions and Complex Fractions.