The equation of type:

**ах² + bxy + c + dx + ey + f = 0**

is** a general type of quadratic equation with two var**iables, in which at least one of the coefficients before the quadra*tic te*rms* *a, b and c is nonzero.

The system:

is a general type of system of one linear and one quadratic equation with two variables. Such a system is solved by the method of substitution, namely, from the linear equation we express one of the variables and replace it in the square.

Example. Let's solve the system of equations:

**2x + y = 1**

**x² + xy + y² = 1**

We express the variable u fr*o*m the first equation:

*у = 1 – 2х*

so by substituting u in the second equation with the expression

**1 – 2x**

you get:

**х² + x (1 – 2х) + (1 – 2х) ² = 1**

after it is solved, Zx – Zx =* 0 is obtained*, ie

*), whose roots ar*

**3x (x – 1**

**e x = 0**,**x = =**1.Substituting these values of x in

*t*o the equation

*u = 1 – 2x,*we obtain the corresponding values fo

*r y*, i.e.

**y₁ = 1**,**y₂ = -1**.So, the solutions of the system are the ordered pairs of numbe

**a**

*rs (0, 1)*

**nd (1, -1**).