# Question #b310b

Oct 9, 2016

$\left(x , y\right) = \left(x , x - 90\right)$

#### Explanation:

Given two variables, at least two equations are needed to determine two unique values for those variables. With only a single equation, we are showing a relationship between the two variables which may be fulfilled by many $\left(x , y\right)$ pairs.

In the given example, we have $x - y = 90$

$\implies x - y + y - 90 = 90 + y - 90$

$\implies y = x - 90$

Thus, for any $x$ value, we can find a corresponding $y$ value which fulfills $x - y = 90$ by setting $y = x - 90$. If we graph this, we get a line, every point of which is an $\left(x , y\right)$ pair satisfying our equation:

graph{x-90 [-275, 333, -168, 136]}

Example $\left(x , y\right)$ pairs:
$\left(- 10 , - 100\right)$
$\left(0 , - 90\right)$
$\left(1 , - 89\right)$
$\left(10 , - 80\right)$
$\left(90 , 0\right)$
$\left(100 , 10\right)$