In maths, an equation is a statement that two things are equal. In an equation, there are two expressions, one on each side of the equal to sign.

**The followings are examples of equations:**

8 + 2 = 10

7 * 5 = 35

12 - 5 = 7

15 / 3 = 5

**Variables in an equation**

Variables are the unknown in an equation. An equation could contain one or more unknowns. In the equation 8 + x = 10, x is the unknown variable. We can now solve this equation to determine the value of x as shown below:

8 + x = 10

x = 10 - 8

Therefore, x = 2

This process of finding the value of the unknown is called solving the equation.

**Practice questions**

Question: Find the value of x in the following equations.

1. 12 - x = 7

2. 13 * x = 26

3. 5 + x = 8

( Answer: 5, 2, 3 )

**Simultaneous equations**

Simultaneous equations are two equations with two unknowns. They are called simultaneous equations because they must be solved together in order to determine the unknowns.

For example:

Given two simultaneous equations x + y = 10 and x - y = 6, find the values of x and y.

Equation 1: x + y = 10

Equation 2: x - y = 6

Add the two equations to eliminate the unknown y

2x = 16

x= 16/2 = 8

Now replace the value of x in equation 1

8 + y = 10

y= 10 - 8 = 2

Answer: x= 8, y= 2

**Solving simultaneous equations using substitution**

Sometimes you can use substitution to solve two simultaneous equations to determine the value of unknowns.

For example:

Given two simultaneous equations x + y = 12 and x = 2y, find the values of x and y.

Equation 1: x + y = 12

Equation 2: x = 2y

Replace the value of x in equation 1

2y + y = 12

3y = 12

y = 4

Now replace the value of y in equation x

x + 4 = 12

x = 8

Answer: x= 8, y= 4

**Practice questions**

Question: Find the value of x and y in the following equations: 3x + y = 7 and 3x - y = 5

( Answer: Equation 1: 3x + y = 7

Equation 2: 3x - y = 5

Now add the two equations

6x = 12

x = 2

Replace the value of x in equation 1

3 * 2 + y = 7

6 + y = 7

y= 1

)

Question: Find the value of x and y in the following equations: y - 2x = 1 and 2y - 3x = 5

( Answer: Equation 1: y - 2x = 1

Equation 2: 2y - 3x = 5

Rearrange equation 1: y = 1 + 2x

Substitute in equation 2: 2 (1 + 2x) - 3x = 5

2 + 4x - 3x = 5

2 + x = 5

x = 3

Use value of x in equation 1

y= 2 * 3 + 1 = 7

)

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