Solve the simultaneous equations. 3x + 5y = 1 , 2x - 3y = 7

3x + 5y = 1   (eq 1)
2x - 3y = 7    (eq 2)

Step 1 -  2* (eq 1) 

6x + 10y = 2  (eq 3)

Step 2 - 3* (eq 2)

6x - 9y = 21  (eq 4)

Step 3  -  eq 4 - eq 3 to cancel the x

-19y = 19 

Therefore, y = -1  (eq 5)

Step 4 - sub (eq 5) back into (eq 1)

3x + 5(-1) = 1

3x - 5 = 1

3x = 6 and therefore x = 2 (eq 6)

Step 5 - Sub (eq 5) and (eq 6) into (eq 2) to check answer.