solve each system

Question

1) 3x + y = 6
2x + 3y = 13

2) 2x + 5y - 6 = 0
-2x + y - 2 = 0

3) x + 3y = 6
4x - 5y = 7

Answer 1

I'll solve the first one, leaving you a chance to practice with the rest.
3x + y = 6 .....(1)
2x + 3y = 13 ....(2)

Multiply (1) by 3 and subtract (2) to eliminate y:

9x + 3y = 18 .....(1a)
2x + 3y = 13 .....(2a)
Subtract:
7x = 5
x=5/7 .....(3)
Substitute (3) in 1
3(5/7) + y = 6
y = 6-15/7
=27/7 ....(4)
Substitute (3) and (4) in (2) to check:
2(5/7) + 3(27/7)
=(10+81)/7
=13 OK.