**Find ordered pairs that satisfy a given equation.**

** **

Each solution to an equation with two variables, such as 2*x *+ 3*y *= 6, will

include two numbers, one for each variable. To keep track of which number

goes with which variable, we write the solutions as ordered pairs. (If *x *and *y*

are used as the variables, the *x*-value is given first.) For example, we can

show that (6, – 2) is a solution of 2*x *+ 3*y *= 6 by substitution.

2** x **+ 3

**= 6**

*y*2(**6**) + 3(-**2**) = 6 ? Let x = 6 , y = -2.

12 – 6 = 6 ?

6 = 6 True

Because the pair of numbers (6, – 2) makes the equation true, it is a solution.

On the other hand, (5, 1) is not a solution of the equation 2*x *+ 3*y *= 6

because

2** x **+ 3

**= 2(**

*y***5**) + 3(

**1**)

= 10 + 3

= 13, ** not **6.