Given that the equation ![-2x+3y=9](https://tex.z-dn.net/?f=-2x%2B3y%3D9)
We need to determine the coordinate that is not a solution to the equation.
<u>Option A</u>: (0,3)
Substituting the coordinate (0,3) in the equation
, we get;
![-2(0)+3(3)=9](https://tex.z-dn.net/?f=-2%280%29%2B3%283%29%3D9)
![0+9=9](https://tex.z-dn.net/?f=0%2B9%3D9)
![9=9](https://tex.z-dn.net/?f=9%3D9)
Since, both sides of the equation are equal, then the coordinate (0,3) is a solution to the equation.
Hence, Option A is not the correct answer.
<u>Option B</u>: (1,-3)
Substituting the coordinate (1,-3) in the equation
, we get;
![-2(1)+3(-3)=9](https://tex.z-dn.net/?f=-2%281%29%2B3%28-3%29%3D9)
![-2-9=9](https://tex.z-dn.net/?f=-2-9%3D9)
![-11\neq 9](https://tex.z-dn.net/?f=-11%5Cneq%209)
Since, both sides of the equation are not equal, then the coordinate (1,-3) is not a solution to the equation.
Hence, Option B is the correct answer.
<u>Option C</u>: (-3,1)
Substituting the coordinate (-3,1) in the equation
, we get;
![-2(-3)+3(1)=9](https://tex.z-dn.net/?f=-2%28-3%29%2B3%281%29%3D9)
![6+3=9](https://tex.z-dn.net/?f=6%2B3%3D9)
![9=9](https://tex.z-dn.net/?f=9%3D9)
Since, both sides of the equation are equal, then the coordinate (-3,1) is a solution to the equation.
Hence, Option C is the correct answer.
Therefore, the coordinate (1,-3) is not a solution to the equation ![-2x+3y=9](https://tex.z-dn.net/?f=-2x%2B3y%3D9)