Solve the simultaneous equations 5x + y = 21, x - 3y = 9

Method 1 - By Elimination: Firstly, understand that in order to eliminate a variable, the coefficient needs to be the same for the variable in both equations. We can eliminate the x variable by multiplying the second equation by 5. This gives us: 5x-15=45.If we now minus the second equation from the first, the 5x-5x cancels out to give 0 and y-(-15y) gives us 16y. So we now understand that 16y = -24. Once we divide both sides by 16, we get y = -1.5. We then substitute this into the original equation, e.g. 5x+(-1.5)=21 then 5x = 22.5. Upon dividing both sides by 5, we get x = 4.5.
Method 2 - By Substitution: We can reorder the second equation to make x the subject which gives us x = 9 + 3y. This can then be substituted as x in the first equation as such: 5(9+3y)+y=21. Upon expanding the brackets, we get 45+16y=21. We then minus both sides by 45 to move it over to the other side: 16y=-24. Which when simplified gives us -3/2 or -1.5.This can then be substituted for y in one of the equations (I'll pick the first) to give us: 5x - 1.5=21 and so 5x = 22.5. When both sides are divided by 5 we get 4.5 as a value for x.