Question about modular equations

[cragar]

Homework Statement

Solve each of the following sets of simultaneous congruences:
{x=1(2),x=2(3),x=3(5),x=4(7)}
{y=1(9),2(5),1(7)}

The Attempt at a Solution

I know how to solve the first one for x but on the second one
with y I am not sure what they mean
so I have y=1mod9 and then 2mod5 should this be equal to y
and same for 1mod7. if there not equal to y does that mean they have to be
fixed at that value, for example 1mod7 would not equal 8 in his case.
or does this mean that y=1mod9 is independent of 2mod5 and 1mod7
so y would simply be 1

 

[mfb]

You are supposed to find a y which satisfies all three equations at the same time. y=1 satisfies the first and third equation, but not the second one.

I wonder how you solved the first one without that knowledge.

 

[cragar]

because on the second one they just write the y one time.
I didnt know if it meant something else.

 

[HallsofIvy]

No, clearly they meant {y=1(9),y=2(5),y=1(7)}. No other interpretation is possible.