00:01
Okay, so for this question, we're asked to solve this system of linear equations or show that this system of equations is inconsistent.
00:11
But to start off, we can try to eliminate the x variable from two of the equations.
00:17
We're going to label these equations 1, 2, and 3, and we can eliminate the x variable from equations 2 and 3 by subtracting multiples over equation 1.
00:30
So the operations we're going to perform here are equation 2 minus 2 times equation 1, and then equation 3 minus 4 times equation 1.
00:45
This will make us get 2x minus 2 times x, so that'll be 0x, and 4x minus 4 times x, which will also give us 0x.
00:56
So starting with our first operation, equation 2 minus 2 times equation 1, we have 2x minus 2 times x.
01:04
0x so we can cross that out it's 0 and we have y minus 2 times negative 2 y that's y plus 4 y is 5 y then we have negative z minus 2 times negative 3 z and that's equal to 2 z or sorry negative z plus 6 z is 5 z and then 5 minus 2 times 5 is negative 5 then for our next operation we have 4x minus 4 times x is 0x so we'll cross that out again then we have negative 3y minus 4 times negative 2y is negative 8 y or sorry that's negative 3y minus negative 2 y is 3 y is 3y negative 3y plus 8 y is equal to 5 y then we have negative 7 z minus 4 times negative 3 z so that's negative 7 z plus 4 plus 12 z is 5 z and then we have 5 minus 4 times 5 is negative 15 so looking at these two new equations we have we call this new equation 2 and the new equation 3 we have 5 y plus 5 z in both of them however we have negative 5 in the first one and negative 15 in the second one this says that 5 y plus 5 z equals negative 5 and that 5 y plus 5 z equals negative 5 and that 5 y plus 5 z equal is negative 15.
03:07
These both can't be true...