Use these 2 simultaneous equations to find x & y: 5y+21=9x and 6x+7y=45

Okay so first, to make the process more simple, I would suggest collecting all algebraic terms on the same side of the question as to get: 9x-5y=21 and 7y+6x=45 (as it already is). Next, looking at both equations, pick either the x or y coefficient and find the lowest common multiple of them i.e. the lowest common multiple of 6 & 9 is 18 so we multiple the first equation by 2 to get 18x-10y=42 and the second equation by 3 to get 21y+18x=135. We do this so we can either add or subtract the equations to eliminate either x or y. In this case, we should take the first equation away from the second: 21y--10y=93 or 31y=93. This simplifies so y=3
Now, we can substitute y=3 into one of the original equations to find x. 5(3)+21=9x therefore 9x=36. Simplifying again, x=4. We can check this by substituting both found variables into the other equation: 6(4)+7(3)=45. As 24+21=45 is true, the answer must be correct.