I'll help with the last three.
13. Multiply the first equation by -4 and add the second.
.. -4(4x -3y) +(16x +10y) = -4(16) +240
.. 22y = 176
.. y = 8
.. x = (16 +3*8)/4 = 10
(x, y) = (10, 8)
14. Divide the first equation by 2, multiply the second by 2, and add.
.. (20x +10y)/2 +2(-5x +4y) = (100)/2 +2(53)
.. 13y = 156
.. y = 12
.. x = (53 -4*12)/-5 = -1
(x, y) = (-1, 12)
18. Multiply the first equation by -2 and the second by 3, then add.
.. -2(3x -5y) +3(2x -3y) = -2(-16) +3(-8)
.. y = 8
.. x = (-16 +5*8)/3 = 8
(x, y) = (8, 8)
