# Algebra Problem With the System of Quadratic Equations in Two Variables

## Find the value of x^2 + y^2 from the system of quadratic equations

If the system of quadratic equations is

x² = 17x + y

y² = x + 17y

x ≠ y

Then find the value of** x² + y² =?**

## Solution

Let

x² = 17x + y …………….eq(1)

y² = x + 17y …………….eq(2)

Add equation 1 and equation 2, then

x² + y² = 17x + y + (x + 17y)

⇒ x² + y² = 18x + 18y

⇒ x² + y² = 18(x + y) ……….eq(3)

Now we need to find x + y to find the value of x² + y²

To find “x + y” subtract equation 2 and equation 1

Thus, x² – y² = 17x + y – (x + 17y)

⇒ x² – y² = 16x – 16y

⇒ (x + y)(x – y) = 16(x – y)

divide with x – y (we know x ≠ y so x – y ≠ 0)

⇒ x + y = 16 …………..eq(4)

From equation 3 and equation 4

x² + y² = 18(x + y)

⇒ x² + y² = 18 × 16

⇒** x² + y² = 288**