# If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

To solve the above equation we will use the substitution method of algebra to systems of linear equations.

## Answer: The value of x - y is 18.

Let's find the value of x - y.

**Explanation:**

Let xy = 144 ---- (1)

and x + y = 30 ---- (2)

From equation (2), we get y = 30 - x

By substitute the value of y = 30 - x in equation (1), we get

⇒ x (30 - x) = 144

⇒ 30 x - x^{2} = 144

⇒ x^{2 }- 30x + 144 = 0

To solve the equation we will factorise the quadratic equation by splitting the middle term.

⇒ x^{2 }- 24 x - 6 x + 144 = 0

⇒ x (x - 24) - 6 (x - 24) = 0

⇒ (x - 6) (x - 24) = 0

By equating both the factors to 0, we will get two values of x.

⇒ x - 6 = 0 or x - 24 = 0

⇒ x = 6 or x = 24

You can use Cuemath's Quadratic Equation Calculator to solve the quadratic equation and find its roots.

Given in the question, x > y.

Therefore, x = 24 and y = 6.

⇒ x - y = 24 - 6 = 18