In details

Solution of a two-variable first degree equation


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

Notice the pairs below:

x = 6, y = 1

x - 2y = 4

6 - 2 . 1 = 4

6 - 2 = 4

4 = 4 (V)

x = 8, y = 2

x - 2y = 4

8 - 2 . 2 = 4

8 - 4 = 4

4 = 4 (V)

x = -2, y = -3

x - 2y = 4

-2 - 2 . (-3) = 4

-2 + 6 = 4

4 = 4 (V)

We found that all these pairs are solutions of the equation x - 2y = 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 3x - y = 8.

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

3x - 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 (r, s) is solution of an equation ax + by = ç (being The and B non-null simultaneously), if for x=r and y=s the sentence is true. Next: Graph of a First Degree Equation with Two Variables