Which ordered pairs in the form (x, y) are solutions to the equation \((x + 6)y = 9\)? Choose all answers that are correct.
A. \((-5, 9)\)
B. \((-3, 3)\)
C. \((3, 1)\)
D. \((7, 9)\)
Answer (3)
So we need to find the solutions to the equation (x+6)y=9 so we can arrange them in pair (x,y). We simply plug in the numbers into the equation. First pair (-5,9), we get (-5+6)9=9 so 1=1 and that is true, so first pair works. Second pair: (-3+6)3=9 we get (3)3=9 and 9=9 so second pair also works. Third pair: (3+6)1=9 we get 9=9, also works. Fourth pair: (7+6)9=9 we get 13*9=9 and 117=9 which is false so the fourth pair can't be a solution for the equation. The correct answers are A, B and C.
To determine which ordered pairs are solutions to the equation (x + 6)y = 9, we substitute the x and y values from each ordered pair into the equation and check for equality.
A. (-5, 9): Substitute x = -5 and y = 9 into the equation: ((-5) + 6)(9) = 1(9) = 9 which is true. Therefore, A is a correct solution.
B. (-3, 3): Substitute x = -3 and y = 3 into the equation: ((-3) + 6)(3) = 3(3) = 9 which is true. Hence, B is a correct solution.
C. (3, 1): Substitute x = 3 and y = 1 into the equation: ((3) + 6)(1) = 9(1) = 9 which is also true. Thus, C is a correct solution.
D. (7, 9): Substitute x = 7 and y = 9 into the equation: ((7) + 6)(9) = 13(9) = 117 which is not equal to 9. Therefore, D is not a correct solution.
The correct answers that satisfy the equation are ordered pairs A (-5, 9), B (-3, 3), and C (3, 1).
The solutions to the equation (x + 6)y = 9 are the ordered pairs: A (-5, 9), B (-3, 3), and C (3, 1). Option D (7, 9) is not a solution. Therefore, the correct answers are A, B, and C.
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