Solve the simultaneous equations 3x + 2y = 12 and 10y = 7x + 16

First we need to rearrange both equations into the form ax + by = c (where a, b and c are the integers). We can label these 1. and 2.We then have:3x + 2y = 12 1.7x -10y = -16 2.In order to find the x value, we need to get rid of the ys. This can be done by multiplying the first equation by 5. This gives us 15x + 10y = 60. 3. We can now easily work with equations 2. and 3. as the y values have the same coefficients.15x + 10y = 60 3.7x - 10y = -16 2.In order to get rid of the y values, we need to add the two equations together (because 10y + (-10y) = 0 )This leaves us with:22x = 44x = 2We can now substitute x = 2 back into equation 1. to find y(3 x 2) + 2y = 122y = 6y =3 Just to be sure, substitute x and y into equation 2. (7 x 2) - (10 x 3) does equal -16. Therefore, the solutions are x= 2 and y=3