00:01
In this problem, we are given the equation negative x plus y plus 2 z equals negative 6 and asked to give four ordered triples that we are able to plug in for x, y, and z on the left side and generate the same number on the left side as on the right side in this particular case, negative 6.
00:23
Now, i think that the easiest way to go about this is to include as many zeros as possible in the order triples in order to leave yourself with a simpler equation.
00:32
Now for example, we might have zero in for x, zero in for y, and an unknown z value.
00:43
Now when we plug in zero for x and y in the equation above, we will see that two, i'll use a different color here, two z is equal to negative six.
01:02
And if we divide both sides by two, we'll see that z is equal to negative 3.
01:12
And so we can plug negative 3 back into the order triple over here.
01:16
And so our first order triple is going to be 0 -0 -9 3.
01:21
Now for our second order triple, we might have another 0 for x, an unknown y value into 0 in for z.
01:35
And so when we plug in 0 for x and z into the equation above, we're going to see that y is equal, to negative 6.
01:49
So we can plug negative 6 into the order triple and get 0, negative 6, 0, as our second order triple...