#### Coefficient

##### New member

- Joined
- Jan 30, 2020

- Messages
- 8

I'm stuck on this question: solve for x (x is an integer) 7x = -19 mod(9) .

Thank you for your help.

- Thread starter Coefficient
- Start date

- Joined
- Jan 30, 2020

- Messages
- 8

I'm stuck on this question: solve for x (x is an integer) 7x = -19 mod(9) .

Thank you for your help.

- Joined
- Nov 12, 2017

- Messages
- 8,888

Then you can just try numbers 1 through 8 to see if any yield a product congruent to the number you found.

- Joined
- Jan 30, 2020

- Messages
- 8

7x ≡ -19[9]

7x ≡ -10[9]

7x ≡ -1[9]

7x ≡ 8[9]

But i couldn't understand how this would help me because the next question is to deduce the solutions of the equation : 7x-9y= -19

Thanks.

- Joined
- Aug 27, 2012

- Messages
- 947

Note that 9y = 0 (mod 9). So the solutions for 7x - 9y = -19 (mod 9) will be the solutions for 7x = -19 (mod 9) and y = anything.

7x ≡ -19[9]

7x ≡ -10[9]

7x ≡ -1[9]

7x ≡ 8[9]

But i couldn't understand how this would help me because the next question is to deduce the solutions of the equation : 7x-9y= -19

Thanks.

-Dan

- Joined
- Jan 30, 2020

- Messages
- 8

Thank youNote that 9y = 0 (mod 9). So the solutions for 7x - 9y = -19 (mod 9) will be the solutions for 7x = -19 (mod 9) and y = anything.

-Dan