At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
first, let's leave the second equation alone for now and just look at m+4n = 8 what do you get when you subtract 4n from each side?
hm, not quite, let's just try the left side first what happens when you subtract 4n from m+4n?
right! now let's look at the right side what happens when you subtract 4n from 8?
nope, since 8 has no variable and 4n has a variable, it's just 8 - 4n understand so far?
ok, so the left side of the equation is m, and the right side of the equation is 8 - 4n, which gives us m = 8 - 4n with me so far?
good, so our first equation is m = 8 - 4n and our second equation is m = n - 2 we have m by itself on the left side in both equations, so we can set the two equations equal to each other 8 - 4n = n - 2 can you try solving for n now?
I thing so would it be 4,6
not quite, let's just take this one step at a time 8 - 4n = n - 2 what happens when you add 2 to each side?
what do you mean
add 2 to the left side, add 2 to the right side, and tell me what is on each side
not quite, remember we want to leave 4n and n alone because these are variables
left side is 8 - 4n, what do you get when you add 2?
great! the right side is n - 2, what do you get when you add 2?
not quite, what is n-2+2?
not quite, think of it this way n-2+2 means start with n, take away 2, then add 2 back what is n-2+2?
not quite, remember that we leave n alone since its a variable one more time n-2+2=?
so basicly we just substract 2 from to then add it back correct
right, so what do we get in the end?
uh, not quite... let me try to explain it differently I start with n marbles. I pick up 2 marbles, then I drop 2 marbles. How many marbles do I have?
hint: I started with n marbles
right! so what does n-2+2=?
good! so, on the left side we have 10-4n and on the right side we have n 10-4n = n now, let's leave 10 alone since it's not a variable what happens when we add 4n to each side?
we get 8n
not quite... the left side is 10-4n, what do we get when we add 4n?
not quite, please try again 10-4n+4n=?
not quite, remember that we leave the 10 alone since it's not a variable (doesn't have n) 10-4n+4n = ?
oh so 10-4n+4n=10-8n
not quite... think of it this way: I start with 10, take away 4n, then add 4n. what's left?
not quite, let's try one more time I start with 10 marbles, then I drop 4n marbles, then I pick up 4n marbles, how many marbles do I have?
14n? I am not sure
let's try something different 10-4+4=?
hint: A-B+B = A
so, if A-B+B = A, then what is 10-4n+4n?
great! so, the left side is 10 now let's move to the right side the right side is n, what do you get when you add 4n?
not quite, remember that we started with n n+4n=?
oh so we just add 4 to the N
not quite... hint: n+4n = (1+4)n
oh so the thing is 5n
great! left side is 10 right side is 5n 10 = 5n can you try solving for n now?
I believe so
I think it would equal 0,2
10 = 5n n = ?
great! n = 2 going back to the original problem, m = n − 2 so what is m?
great! m=0 n=2 so what is (m,n)?
great, we're done!