00:01
In this problem, we are given the equation 2x minus y plus 3z equals negative 12, and asked to provide four ordered triples that we are able to plug in for the x, y, and z values, and generate the same number on the left side as on the right side, namely negative 12.
00:23
Now, i believe that the easiest way to go about this is to have as many zeros in order triples as possible in order to give yourself a simpler equation to solve.
00:34
Now, for example, our first order triple might be zero, zero, and then have an unknown z value.
00:44
Now, if we plug in zero for x and y, we're going to get 3z equals negative 12.
00:53
Now we can divide both sides by three and get that z is equal to negative 4.
01:01
And so we can put negative 4 in this triple over here and get 0 -0 -0 -9 -4 as our first order triple.
01:09
Now our second order triple might be 0, an unknown y value, and a 0 for z.
01:21
And so when we plug in 0 for x and z, we'll see that negative y is equal to negative 12.
01:31
And you can either divide or multiply both sides by negative 1 and get that y, is equal to 12.
01:41
And so we can put 12 in for the y value and get 0, 12, 0 as our second order triple.
01:48
Now for our third order triple, if you can see the pattern, we'll leave the x value blank, but a 0 in for y and a 0 in for z.
02:00
Now when we plug in 0 for y and z, to the equation above, we'll see that 2x is equal to negative 12...