00:01
In this problem, we are told that if you add together the gestation periods of an elephant, a rhino, and a camel, you will get 1 ,520 days.
00:12
And so in this particular example, the gestation period of an elephant is represented by e, a rhino is represented by r and of a camel is represented by c.
00:22
And so that's where you get the equation, e plus r plus c, equals 1 ,520.
00:28
And we're also told that if you take a camel's gestation period and add 58 days to it, you get the gestation period of a rhino, which is where the second equation comes from.
00:41
And then we're also told that if you take a camel's gestation period, multiply it times two, and then subtract 162 days from that, you'll get the gestation period of an elephant, and that's where we get this third equation.
00:56
Now we're going to rewrite these equations to have all of the variables always on the left side of the equation and all of the constants always on the right side.
01:06
And that way we can treat them as we would a normal system of equations.
01:10
And so when we do this, we're going to treat e as x, r as y, and c as z.
01:20
You can choose whichever one to assign to whichever normal variable we're used to seeing.
01:28
In this case, i'm going to do it the way.
01:31
That i just said and so when we subtract r from both sides and subtract 58 we get negative r plus c is equal to negative 58 and then for the third equation we're going to subtract e from both sides and add 162 to both sides and when we do that we'll see that negative e plus 2c is equal to 162 and now we're going to the first equation, the e specifically, to eliminate the e in the third equation, because we don't have an e in the second equation.
02:22
And so when we do this, all we have to do is take the first equation and add it to the third equation to make the coefficient in front of the e in the third equation zero.
02:31
And when we rewrite our equations, our first and second equations are going to stay the same.
02:47
And our third equation becomes e plus negative e that's 0e.
02:51
We get r plus 0, r, that's just and we get c plus c that's 3c and then we get 1520 plus 1622 that is 1 ,682 okay and now we're going to want to eliminate the r the third equation now normally we would want a negative 1 right here as the coefficient for r and so what we're going to do is you can swap the second and third equations if you want to however it is also just simple to multiply the second equation times negative 1.
03:37
And when we rewrite all of the equations, we get the same first equation.
03:48
The second equation now becomes r minus c equals 58.
03:59
And the third equation is r plus 3c is equal to 1 ,682.
04:10
Now if you had noticed that if we just added back here, the second equation to the third equation, you could have done that.
04:17
However, i also think it's always good to make the coefficient if we're able to of the r and the second equation 1.
04:27
And so now we're going to take the second equation, multiply times negative 1, and add it to the third equation in order to eliminate the r and the third equation.
04:37
And when we do that, we get the same first equation, the same second equation as well, and the third equation becomes negative r plus r, that's zero r.
04:57
And we get negative 1 times negative c, that's c, out of it to the 3c, and the third equation we get 4c.
05:04
And we get negative 1 times 58, add that to 1682, we get 1 ,60024...