00:01
We know solve this system of equations.
00:04
So here we have three equations.
00:07
Let's number the equations as this one is number one.
00:11
This is equation number two.
00:13
And then we write this as equation number three.
00:17
So we can use substitution or elimination method to solve this system of equation.
00:23
Looking at this system, that is equation number three, we see that this equation has only x and z variables it doesn't have y variable which means we need one more equation as like this so that we can eliminate one of the variables and solve for one of the variables so let's consider the first two equation and eliminate y eliminating y from these two equations gives us an fourth equation involving only x and z variable so using the fourth equation and also the third equation we can solve for either x or z and then solve for other variables as well.
01:04
So first, let's eliminate wife using the equation number 1 and 2.
01:10
For that, i'm going to multiply the equation number 1 by negative 2.
01:15
So i write equation number 1 multiplied with negative 2.
01:19
And this gives 2 times negative 2 is negative 4.
01:23
It's negative 4x.
01:25
And here the coefficient of y is 1.
01:28
So 1 times negative 2 is negative 2.
01:31
So it is negative 2 .y.
01:33
And 3 times negative 2 is negative 6 z.
01:36
And this equals 20 times negative 2 is negative 40.
01:40
Now let me write the equation number 2 as it is.
01:44
So this is written without any chain.
01:47
That is x plus 2y minus z.
01:51
And this equals negative 11.
01:53
Now let's add these two equation.
01:56
So here.
01:58
You'll see this negative 4x, positive x is negative 3x.
02:05
And then negative 2y, positive 2y becomes cancelled.
02:09
And then we have negative 6 z, negative z is negative 7 z.
02:16
And this equals negative 40, negative 11 is negative 51.
02:19
So we have obtained an equation in variable x and z.
02:24
Let's see this is equation number 4.
02:27
Now we can eliminate one of the variable using equation number 3 and 4 so that we can solve for one variable.
02:36
Looking at these two equations, we clearly see that here we have 3x and this one is negative 3x.
02:43
So we just have to add these two equations so that x variable will get eliminated...