Algebra Math Problem

If x = 2x² + y and x − y = 2, then find the value of x and y

x=2x^2+y

x-y=2

x=?? \ \ \ y=??

Solution

We can solve this problem using quartratic equation

x = 2x² + y

⇒ y = x − 2x²……………eq(1)

x − y = 2 ……………eq(2)

From equation 1 & equation 2

x − y = 2

⇒ x − ( x − 2x² ) = 2

⇒ 2x² = 2

⇒ x² = 1

This is a quadratic equation, take square roots in both sides

⇒ x = ±1

When x = 1

y = 2 − 1 = 1

When x = −1

y = 2 + 1 = 3

So

Solution to two variable quadratic equation (x, y) = (1, −1), (−1, 3)