the answer is 5,-3 how: because there arnt like terms in the two equations you find which number you can military to the equations to make one of the numbers the same. in this case i multiplied the top equation by -2y from the bottom equation (5x-3y=16)^-2 then multiplied the bottom equation by 3y (4x-2y=14)^-3 both equations multiplied are (-10x+6y=-32) and (-12x+6y=-42) now that we have two of the same terms (6y) they are the same signs (both positive) so we switch the sign on the bottom equation. (12x-6y=42) and because there the same we subtract the equations. (-10x+6y=-32) - (12x-6y=42)= 2x=10. the y cancels out. and now we divide 2 by 2x and that leaves x then we divide 2 by 10 =5 so your x=5 to find y we take any ORIGINAL equation im using (4x-2y=14) we use our x and replace 4x to 4(5)=20x making our new equation (20x-2y=14) we subtract -20 to 20 . cancels out 20 and leaves us with 2y=14 then subtract 20 it to 14. which gives us -6 (-2y=-6) divide -2y by -2 which gives us y alone. then divide -2 by 6 gives -3. (y=-3) making (5,-3) your answer.
