3y=x+1 2y+x=9

3y  =  x + 1

2y + x = 9

If you solve the first equation for x, you get:  3y -1  =  x

If you solve the second equation for x, you get  x  =  9 - 2y

Since they are both solved for x, you can set them equal to each other:  3y - 1  =  9 - 2y

--->   3y - 1  =  9 - 2y

Add 2y to both sides:

--->   5y - 1  =  9

Add 1 to both sides:

--->   5y  =  10

Divide both sides by 5:

--->   y  =  2

Substitute this value back into either equation:  3y  =  x + 1   --->   3(2)  =  x + 1

     --->   6  =  x + 1     --->   x  =  5