# Online Algebra Tutoring: Linear Equations

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## Learn Linear Equations from Certified Online Algebra Tutor

A set of different linear equations having the same pair of variables and satisfying the same conditions is a system of Linear Equations.

A system can have 2 or more Linear Equations. The simplest system is when we have 2 Linear Equations in 2 variables.

**For example:**

**2x + y = 10**

**y – x = 16**

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**Here, we have a set of 2 linear equations in 2 variables x and y.**

Solving two Simultaneous Linear Equations means finding the values of x and y that satisfy both the given equations. Hence, it is important that both equations have the same pair of variables and the equations are linear.

Solution **(x, y)** of a system of Linear Equations is the point **(x, y)** where the graphs (lines) of all those linear equations intersect.

**Methods to solve Simultaneous Linear equations**

There are different methods to solve simultaneous Linear equations.

- Substitution Method
- Elimination Method
- Graphing method
- Matrix method

**Checkpoint:**

Can the following pair of equations be solved?

1. x + y = 20

x + z = 30

2. 2x = 6

3y = 12

3. x² + y = 4

2x – 8 = y

4. x = 7 – 5y

m = 7 – 5n

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