Find ordered pairs that satisfy a given equation.
Each solution to an equation with two variables, such as 2x + 3y = 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 2x + 3y = 6 by substitution.
2x + 3y = 6
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 2x + 3y = 6
because
2x + 3y = 2(5) + 3(1)
= 10 + 3
= 13, not 6.