# Can You Solve the Two Variable Quadratic Equation

# Algebra Math Problem

### If *x = *2*x² + 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 *=* *2*x² *+* y*

⇒ *y* =* x − *2

*x²*……………

*eq(1)*

*x − y *=* *2 ……………*eq(2)*

From equation 1 & equation 2

*x − y *=* *2

⇒ *x − *(* x − *2

*x²*)

*= 2*

⇒ 2* x² *= 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)**