# 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).**

### Checkpoint:

#### 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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