how to solve linear equations in two variables by elimination The elimination method is a technique for solving systems of linear equations Let s walk through a couple of examples Example 1 We re asked to solve this system of equations 2 y 7 x 5 5 y 7 x 12 We notice that the first equation has a 7 x term and the second equation has a 7 x term
Add the two equations to eliminate y The resulting equation has only 1 variable x Solve for x the remaining variable Substitute x 11 into one of the original equations Solve for the other variable y Write the solution as an ordered pair The ordered pair is 11 1 Check that the ordered pair is a solution to both original equations Solve the system by elimination x 1 2 y 6 3 2 x 2 3 y 17 2 x 1 2 y 6 3 2 x 2 3 y 17 2 Solution In this example both equations have fractions
how to solve linear equations in two variables by elimination
how to solve linear equations in two variables by elimination
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Add the equations resulting from Step 2 to eliminate one variable Solve for the remaining variable Substitute the solution from Step 4 into one of the original equations Then solve for the other variable Write the solution as an ordered pair Check that the ordered pair is a solution to both original equations I know three easy steps to solve these type of equations by elimination method 1 equation must always start with the same variable 2 find the co efficient of each variable 3 cross multiply each equation using the variables
In some cases we need to slightly manipulate a system of equations before we can solve it using the elimination method See how it s done in this video Created by Sal Khan We have developed three methods for solving linear systems of two equations with two variables In this section we summarize the strengths and weaknesses of each method The graphing method is useful for understanding what a system of equations is and what the solutions must look like
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What is the Elimination Method It is one way to solve a system of equations The basic idea is if you have 2 equations you can sometimes do a single operation and then add the 2 equations in a way that eleiminates 1 of the 2 variables as the example that follows shows Step 1 The first step is to multiply or divide both the linear equations with a non zero number to get a common coefficient of any one of the variables in both equations Step 2 Add or subtract both the equations such that the same terms will get eliminated
Example 1 Solve this system of equations by using elimination Arrange both equations in standard form placing like terms one above the other Select a variable to eliminate say y The coefficients of y are 5 and 2 These both divide into 10 Arrange so that the coefficient of y is 10 in one equation and 10 in the other 2x y 15 3x y 5 2 x y 15 3 x y 5 The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently In this example the ordered pair 4 7 is the solution to the system of linear equations
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how to solve linear equations in two variables by elimination - I know three easy steps to solve these type of equations by elimination method 1 equation must always start with the same variable 2 find the co efficient of each variable 3 cross multiply each equation using the variables