Determine the ordered pair that satisfies the equation, -5x - 6y = -8.
To determine the ordered pair that satisfies the equation, -5x - 6y = -8, we can use any method of solving linear equations, such as substitution or elimination. In this case, we will use the substitution method.
Step 1: Solve for one variable in terms of the other.
-5x - 6y = -8
Let's solve for x:
-5x = 6y - 8
Divide both sides by -5 to isolate x:
x = (6y - 8) / -5
Step 2: Substitute the expression for x into the equation.
Now, substitute (6y - 8) / -5 for x in the equation -5x - 6y = -8:
-5[(6y - 8) / -5] - 6y = -8
Step 3: Simplify and solve for y.
Multiply -5 by (6y - 8) and distribute:
6y - 8 - 6y = -8
Combine like terms:
-8 = -8
Step 4: Determine the ordered pair.
Since -8 = -8 is a true statement, this means the equation -5x - 6y = -8 is true for all values of x and y. Therefore, any ordered pair of the form (x, y) will satisfy the equation.
In other words, there are infinitely many ordered pairs that satisfy this equation. One way to express these solutions is by parameterizing one of the variables. For example, we could choose y as the parameter and express x in terms of y:
x = (6y - 8) / -5
So, the ordered pair in terms of y would be:
(x, y) = ((6y - 8) / -5, y)
For any value of y you choose, you can substitute it into this expression to get the corresponding values for x and y.
x = -2
y = +3