What are the values of *x *and *y* that make the sentence *x* - 2*y* = 4 true?

Notice the pairs below:

**x**** = 6, y = 1**

*x* - 2*y* = 4

6 - 2 . 1 = 4

6 - 2 = 4

4 = 4 ** (V)**

**x**** = 8, y = 2**

*x* - 2*y* = 4

8 - 2 . 2 = 4

8 - 4 = 4

4 = 4 **(V)**

**x**** = -2, y = -3**

*x* - 2*y* = 4

-2 - 2 . (-3) = 4

-2 + 6 = 4

4 = 4 **(V)**

We found that all these pairs are **solutions** of the equation *x* - 2*y* = 4. Thus, the pairs (6, 1); (8,2); (-2, -3) are some of the solutions of this equation.

A two-variable first degree equation has **endless solutions** - infinite (*x*, *y*) -, therefore being its universe .

We can determine these solutions by assigning any values to one of the variables and then calculating the value of the other. Example:

Find a solution for equation 3

*x*-*y*= 8.

We attribute to *x* value 1, and calculate the value of *y*. Like this:

3*x* - *y* = 8

3 . (1) - *y* = 8

3 - *y* = 8

-*y* = 5 ==> **We multiply by -1**

*y* = -5

Pair (1, -5) is one of the solutions of this equation.

*V* = {(1, -5)}

Summing up:

An ordered pair**(**is solution of an equation

*r*,*s*)*ax*+

*by*=

*ç*(being

*The*and

*B*non-null simultaneously), if for

**x****=**and

*r*

**y****=**the sentence is true. Next: Graph of a First Degree Equation with Two Variables

*s*