The number of boys in ninth grade is 12 less than twice the number of girls. there are 51 students in ninth grade. how many are girls?

X- amount of girls
y-amount of boys

x+y=51
y+12=2*x

From first equation:
x=51-y

substitude to second:
y+12=2*(51-y)

y+12=102-2y
3y=102-12

3y=90 /:3
y=30

x=51-30=21 

There are 21 girls.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.