Answer
x, y, equation, (2,1)
Work Step by Step
So this is a fill-in-the-blank question.
The system of equations... is a system of two equations in the two variables (x) and (y)... we check whether x = 5 and y = -1 satisfy each (equation) in the system.
The question then asks whether the following are solutions of the system:
Given:
$2x + 3y = 7$
$5x - y = 9$
(5,-1)
$2 (5) + 3(-1) = 7$ True
$5 (5) - (-1) = 9$ False
(-1, 3)
$2(-1) + 3(3) = 7$ True
$5 (-1) - 3 = 9$ False
(2,1)
$2(2) + 3(1) = 7$ True
$5 (2) - 1 = 9$ True
Thus $(2,1)$ is the only answer