The ordered pairs [tex](-9, -12)[/tex], [tex](1, -4)[/tex] and [tex](6, 0)[/tex] are solutions to the equation [tex]4\cdot x - 5\cdot y = 24[/tex].
In this question we must evaluate the linear equation on each ordered pair. A ordered pair belongs to the function if and only if equivalence exists. Now we proceed to check each ordered pair:
(x, y) = (-9, -12)
[tex]z = 4\cdot (-9) -5\cdot (-12)[/tex]
[tex]z = -36 + 60[/tex]
[tex]z = 24[/tex]
(x, y) = (1, -4)
[tex]z = 4\cdot 1 -5\cdot (-4)[/tex]
[tex]z = 4 + 20[/tex]
[tex]z = 24[/tex]
(x, y) = (4, 8)
[tex]z = 4\cdot (4) - 5\cdot (8)[/tex]
[tex]z = 16 - 40[/tex]
[tex]z = -24[/tex]
(x, y) = (6, 0)
[tex]z = 4\cdot (6) - 5\cdot (0) = 24[/tex]
[tex]z = 24 - 0[/tex]
[tex]z = 24[/tex]
The ordered pairs [tex](-9, -12)[/tex], [tex](1, -4)[/tex] and [tex](6, 0)[/tex] are solutions to the equation [tex]4\cdot x - 5\cdot y = 24[/tex].
We kindly invite to check this question on ordered pairs: https://brainly.com/question/16183359
