Question

for each ordered pair, determine whether it a solution to the systems of equations
-9x+2y+6
5x-3y=8

(x,y) is it a solution? yes/no
(5,-4)
(-6,-2)
(0,3)
(7,9)

Answer 1

that wasnt correct

Answer 2

To determine whether each ordered pair is a solution to the system of equations, we need to check if the values of x and y make both equations true.

1. (5,-4)
-9(5) + 2(-4) = -45 - 8 = -53 ≠ 6
5(5) - 3(-4) = 25 + 12 = 37 ≠ 8
No, it is not a solution.

2. (-6,-2)
-9(-6) + 2(-2) = 54 - 4 = 50 ≠ 6
5(-6) - 3(-2) = -30 + 6 = -24 ≠ 8
No, it is not a solution.

3. (0,3)
-9(0) + 2(3) = 0 + 6 = 6
5(0) - 3(3) = 0 - 9 = -9 ≠ 8
No, it is not a solution.

4. (7,9)
-9(7) + 2(9) = -63 + 18 = -45 ≠ 6
5(7) - 3(9) = 35 - 27 = 8
Yes, it is a solution.

Therefore, the ordered pairs (5,-4), (-6,-2), and (0,3) are not solutions to the system of equations, while (7,9) is a solution.

Answer 3

Apologies for the mistake. Let's re-evaluate the solutions to the system of equations:

1. (5,-4):
-9(5) + 2(-4) = -45 - 8 = -53 ≠ 6
5(5) - 3(-4) = 25 + 12 = 37 ≠ 8
No, it is not a solution.

2. (-6,-2):
-9(-6) + 2(-2) = 54 - 4 = 50 ≠ 6
5(-6) - 3(-2) = -30 + 6 = -24 ≠ 8
No, it is not a solution.

3. (0,3):
-9(0) + 2(3) = 0 + 6 = 6
5(0) - 3(3) = 0 - 9 = -9 ≠ 8
No, it is not a solution.

4. (7,9):
-9(7) + 2(9) = -63 + 18 = -45 + 18 = -27 ≠ 6
5(7) - 3(9) = 35 - 27 = 8
No, it is not a solution.

Therefore, none of the ordered pairs (5,-4), (-6,-2), (0,3), and (7,9) are solutions to the system of equations.