00:02
So in this problem, we want to solve the system of linear equations.
00:06
X1 minus 3x2 plus 4x3 is equal to negative 4.
00:12
3x1 minus 7x2 plus 7x3 is negative 8, and negative 4x1 plus 6x2 minus x3 is 7.
00:21
So a trick to solving systems of linear equations is to try and eliminate terms.
00:27
So we can eliminate the term x1 for a bit by multiplying this by three and then subtracting it from this.
00:38
See, if we multiply this by three, then we'll have three x1s, and then when we subtract, we won't have any more x1 terms anymore.
00:48
So once we have subtracted the second line from three times the first line, then the left -hand side will.
00:58
We've already eliminated this because 3x1 minus 3x1 is 0.
01:03
So we're left with negative 7x2 plus 7x3 minus minus 3 times negative 3x2 plus 4x3.
01:17
And we know from the right hand side that that will equal to negative 8 minus 3 times negative 4.
01:25
So simplifying that we get a new equation we can use...