00:01
We're looking to solve this system of equations.
00:04
I'm going to start by combining the second and third equation, and i'm going to eliminate the y's because that way i can combine it with the first equation.
00:15
In order to combine them, i'm going to multiply the second equation by negative one, because if i do that, the negative one y will turn into a positive one y, which i can then add to the the first second equation to get zero.
00:34
So multiplying the last equation by negative one gives me negative 6x plus y minus 5z equals negative 10.
00:48
Adding them together, i have negative 3x minus 6z equals negative 9.
01:00
Now let's take the first equation, and let's multiply everything by three to get a solution.
01:14
Multiplying x times three gives me 3x.
01:21
Multiplying 2z times three gives me 6z, and multiplying three by three gives me nine.
01:31
That will give us zero equals zero.
01:37
Now zero equals zero is a true statement.
01:40
What this is telling us then is that there are infinitely many solutions.
01:51
Now if we wanted to put those solutions in terms of x, we do have the first coordinate of x.
02:00
Z we can find from the top equation.
02:06
If we wanted to write z in terms of x, i could simply solve that equation for z.
02:18
X plus 2z equals 3.
02:20
Subtract the x, divide by the 2.
02:30
So if i divide both by 2, z is three halves minus one half x.
02:38
To figure what y is in terms of x, i could go to either equation and fill in both x and z...