00:01
Unique solution, write the solution set, otherwise determine the number of solutions to the system and determine whether a system is inconsistent or the equations are dependent.
00:08
So first of all, i did this separately, and this should have an x next to it.
00:14
The first thing i did is i multiplied this whole equation by four, this whole equation by eight, and this whole equation by two, so that way i could get rid of the fractions.
00:26
And so when i did that, my new equation were 4x minus 3y plus 5 z equals 15 and then negative 2x plus 4y plus z equals negative 19 and then negative 5x plus 9y plus 2 z equals negative 42 okay so that was a first step.
01:06
Then the next step, i noticed that this equation i could solve for z.
01:10
So i would get z equals 2x minus 4y minus 19.
01:20
Then what i did was, i'm just going to change my color here for a minute, i took this part of the equation and i plugged it into z in this top equation and this bottom equation.
01:33
And so i had 4x minus 3y plus 5 multiplied by the quantity of 2x minus 4y minus 19 equals 15.
01:50
And then once i distributed and combined like terms, i got negative x plus y plus y equals 4.
02:04
And then to this bottom equation, i had negative 5x plus 9y plus 2 multiplied by the quantity of 2x minus 4y minus 19 equals the negative 42.
02:19
And the equation that i got, once i simplified, i got 14x minus 23y equals 110...