Define x and y if 2x+y=16 and 4x+6y=24

These are a pair of simultaneous equations.First, we can equate two of the coefficients in each equation (let's choose x) by multiplying each equation respectively.With our first equation, multiply it by 2: 4x+2y=32We can leave the second equation as before: 4x+6y=24
As the signs of the coefficients of x in both equations are positive we subtract the second equation from the first to obtain -4y=8 and so y=-2
We can then substitute this value of y into one of our original equations:2x+y=16, 2x-2=16, 2x=18, x=9
Therefore x=9 and y=-2.
We can check this solution by inputting the values of x and y into our second equation:4x+6y=24, 4(9)+6(-2)=24. This holds and so our values of x and y are correct.