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# Online Algebra Tutoring: Simultaneous Equations 1

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### Learn Simultaneous Equations 1 from  Online Algebra Tutor

In this method, we eliminate one variable (say x) to find the value of the other variable (y) and then put back the value of y in the original equation to find the value of the x . This can be done by adding the equations if they have the opposites (like 2y and – 2y are opposites). Let us see how this method works with an example

### Example:

Solve system of linear equations by elimination method 2x + 3y = 15 equation 1 x – 3y = 3 equation 2 Step 1: These are two equations, we will first line up the variables (if they are not lined up) 2 x + 3y = 15 x – 3y = 3 Step 2: Here we have opposites 3y and – 3y , so we will simply add the equations to eliminate y variable 2 x + 3 y = 15 x – 3y = 3 3 x = 18 x = 6 Step 3: Putting this value back of x into any one original equation. We are putting in equation 2 x – 3y = 3 6 – 3y = 3 -3y = 3 – 6 -3y = -3 y = 1 Solution x = 6 , y = 1 or (6 , 1).

## Check Point

Solve these systems of Equations by Elimination method

1. 2x – y = 17, x – y = 10
2. –2x + y = 10, 4x – y = –14
3.  –x – 3y = 18, 2x + 3y = –12
4.  2x + 7y = 21, 3x + 7y = 14
5.  y = −4x – 18 , y = 4x + 22

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