# Thread: How Do I solve This?

1. ## How Do I solve This?

Hi everyone,

I am trying to find all the solutions for the following system :

$\displaystyle x \equiv 1 (mod 2) \\ x \equiv 2 (mod 3) \\ x \equiv 3 (mod 5) \\ x \equiv 5 (mod 7)$

[All the x's begin with new line. I'm finding it hard to include newlines that is why.]
I learnt it follows the following pattern:

$\displaystyle x = a_{1}M_{1}y_{1} + a_{2}M_{2}y_{2} + a_{3}M_{3}y_{3} + a_{4}M_{4}y_{4}$

My problem now is how to find the M's and the y's. I am finding it hard to calculate the M's and the y's.

I need some explanation to solve it.

2. Originally Posted by kap
Hi everyone,

I am trying to find all the solutions for the following system :

$\displaystyle x \equiv 1 (mod 2) \\ x \equiv 2 (mod 3) \\ x \equiv 3 (mod 5) \\ x \equiv 5 (mod 7)$

[All the x's begin with new line. I'm finding it hard to include newlines that is why.]
I learnt it follows the following pattern:

$\displaystyle x = a_{1}M_{1}y_{1} + a_{2}M_{2}y_{2} + a_{3}M_{3}y_{3} + a_{4}M_{4}y_{4}$

My problem now is how to find the M's and the y's. I am finding it hard to calculate the M's and the y's.

I need some explanation to solve it.