Can You Solve the Two Variable Quadratic Equation
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)