The sum of two numbers is 50, and their difference is 30. Find the numbers.

The sum of two number is 50 and their difference is 30 then the two numbers are either 40 and 10 or 10 and 40.

Let us suppose the numbers are x and y then the two equation formed by above statement are x + y = 50 and x – y = 30 . This is linear equation in two variables x and y. After solving these two equation we get the numbers as 40 and 10 or 10 and 40. The linear equation formed in two variables are :

The sum of the two numbers is 50 i.e.,

x + y=50 . . .(i)

The difference between the two numbers is 30 i.e.,

∣x−y∣ = 30 . . . (ii)

From equation i, we can express y in terms of x we get,

y = 50 − x

Putting this value Substituting this expression for y into another equation , we get,

∣x − (50−x)∣ = 30

∣x − 50 +x∣ = 30

∣2x − 50∣ = 30

2x − 50 = ±30

2x = 50 ± 30

⇒ x = 40 or x = 10.

For x = 40 we get y = 10 and for x = 10 we get y = 40.

This equation has two possible solution. The two numbers are either 40 and 10, or 10 and 40.

What are Linear Equations?

Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2 = 5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

• 4x = 8
• 5x + 10 = -20
• 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0

Here,

• The numbers ‘a’ and ‘b’ are real.
• Neither ‘a’ nor ‘b’ are equal to zero.

Read more about Linear Equations.