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The 1st degree equations that present only one unknown respect the following general form: ax + b = 0, with a ≠ 0 and variable x. 1st degree equations with two unknowns present a different general form, as they depend on two variables, x and y. Note the general form of this type of equation: ax + by = 0, with a ≠ 0, b ≠ 0 and variables forming the ordered pair (x, y).

In the equations where the ordered pair exists (x, y), for each value of x we have a value for y. This occurs in different equations, since from equation to equation the numerical coefficients a and b assume different values. Take a look at some examples:*Example 1 *

Let's build a table of ordered pairs (x, y) according to the following equation: 2x + 5y = 10.**x = –2**

2 * (–2) + 5y = 10

–4 + 5y = 10

5y = 10 + 4

5y = 14**y = 14/5****x = -1**

2 * (–1) + 5y = 10

–2 + 5y = 10

5y = 10 + 2

5y = 12**y = 12/5****x = 0**

2 * 0 + 5y = 10

0 + 5y = 10

5y = 10

y = 10/5**y = 2****x = 1 **

2 * 1 + 5y = 10

2 + 5y = 10

5y = 10 - 2

5y = 8**y = 8/5 **

**x = 2**

2 * 2 + 5y = 10

4 + 5y = 10

5y = 10 - 4

5y = 6

**y = 6/5**

*Example 2*Given the equation x – 4y = –15, determine the ordered pairs obeying the numerical range –3 ≤ x ≤ 3.

**x = –3**

–3 – 4y = – 15

– 4y = –15 + 3

– 4y = – 12

4y = 12

**y = 3**

**x = – 2**

–2 – 4y = – 15

– 4y = –15 + 2

– 4y = – 13

4y = 13

**y = 13/4**

**x = – 1**

–1 – 4y = – 15

– 4y = –15 + 1

– 4y = – 14

4y = 14

**y = 14/4 = 7/2**

**x = 0**

0 – 4y = – 15

– 4y = – 15

4y = 15

**y = 4/15**

**x = 1**

1 – 4y = – 15

– 4y = – 15 – 1

– 4y = – 16

4y = 16

**y = 4**

**x = 2**

2 – 4y = – 15

– 4y = – 15 – 2

– 4y = – 17

4y = 17

**y = 17/4**

**x = 3**

3 – 4y = – 15

– 4y = – 15 – 3

– 4y = – 18

4y = 18

**y = 18/4 = 9/2**

by Mark Noah

Graduated in Mathematics

**Source:** Brazil School - https://brasilescola.uol.com.br/matematica/equacao-1-o-grau-com-duas-incognitas.htm