Simultaneous equations can be solve,

- Elimination method
- Substitution method

*Elimination method*Ex:

**4x + y = 9 ----------------- (1)**

**x – y = 1 ----------------- (2)**

Step 1: Make the coefficients of the same in one of the variables in both equations. As you can see in the example variable “y” coefficients is 1 and -1. So we can simply eliminate “y” by adding two equations.

(1) + (2)

4x + y + x – y = 9 + 1

5x = 10

x=

**2**

Now we can apply x in one of the equation (1 or 2), applying x for equation (1)

4 * 2 + y = 9

Y =

**1**

Now we can apply x and y in equations two and verify the results are fine.

*Substitution method*This is more reliable method when solving hard questions.

Ex:

**4x + y = 9 ----------------- (1)**

**x – y = 1 ----------------- (2)**

Step 1: First define one variable from other variable in equation (1)

Y = 9 – 4x ----------------- (3)

Now apply equation (3) in equation (2)

x – y = 1

x – (9 – 4x) = 1

x - 9 + 4x = 1

5x = 10

x=

**2**

Apply x in equation (3)

y = 9 – 4*2

y =

**1**

Now verify your result applying in equation (1)

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