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Write one equation above the other by matching up the x and y variables and the whole numbers. When you use the multiplication method, none of the variables will have matching coefficients -- yet. 3x + 2y = 10 2x - y = 2 Now, multiply one or both of the equations by a number that would make one of the variables have the same coefficient. In this case, you can multiply the entire second equation by 2 so that the variable -y becomes -2y and is equal to the first y coefficient. Here's how to do it: 2 (2x - y = 2) 4x - 2y = 4 Now, just use the addition or subtraction method on the two equations based on which method would eliminate the variable with the same coefficient. Since you're working with 2y and -2y, you should use the addition method because 2y + -2y is equal to 0. If you were working with 2y and positive 2y, then you would use the subtraction method. Here's how to use the addition method to eliminate one of the variables: 3x + 2y = 10 + 4x - 2y = 4 7x + 0 = 14 7x = 14 Just solve to find the value of the term that you haven't eliminated. If 7x = 14, then x = 2. Plug the term back into one of the original equations to solve for the other term. Pick the easier equation to do it faster. x = 2 ---> 2x - y = 2 4 - y = 2 -y = -2 y = 2 You have solved the system of equations by multiplication. (x, y) = (2, 2) To check your answer, just plug the two values you found back into the original equations to make sure that you have the right values. Plug (2, 2) in for (x, y) in the equation 3x + 2y = 10. 3(2) + 2(2) = 10 6 + 4 = 10 10 = 10 Plug (2, 2) in for (x, y) in the equation 2x - y = 2. 2(2) - 2 = 2 4 - 2 = 2 2 = 2
Write one equation above the other. Multiply one or both equations until one of the variables of both terms have equal coefficients. Add or subtract the equations. Solve for the remaining term. Plug the term back into the equation to find the value of the first term. Check your answer.