# 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**

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

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