How to solve the simultaneous equations: 3x+5y=19 and 4x+6y=22

First find a shared factor between the x's or the y's. Both 5 and 6 are a factor of 30. So 30/5 is 6 therefore we multiply the whole of equation 1 by 6 to get 18x+30y=114. Then 30/6 =5 so we multiply the whole of the second equation by 5 which is 20x+30y=110. Minus the second equation from the first equation (114-110=4, 18x-20x=-2x, 30y-30y=0) gets us -2x=4 (we have eliminated y in order to find x). This gives x-2. We then plug that back into either equation to get 3(-2)+5y=19 therefore 5y=25 so y is 5.