Question 1142298
<pre>use Cramer's rule to solve this linear system.

{{{system(5x+10y=70,
5x+25z=270, 
10y+25z=300

)}}}

Write it this way with 0 coefficients for the missing letters:

{{{system(5x+10y+0z=70,
5x+0y+25z=270, 
0x+10y+25z=300

)}}}

We begin by finding the determinant {{{D}}}. It consists 
of just the three columns of x, y, and z coefficients,
in that order, but does not contain the constants, the
three numbers to the right of the equal signs.

{{{D=abs(matrix(3,3,5,10,0,5,0,25,0,10,25))}}}.

It has value {{{D=-2500}}}.

Next we find {{{D[x]}}}.

D<sub>x</sub> has all the same elements as D except that the 1st column is replaced by
the three numbers that occur after the equal signs in the system, in the
order that they occur top to bottom:

{{{D[x]=abs(matrix(3,3,70,10,0,270,0,25,300,10,25))}}}.

It has value {{{D[x]=-10000}}}.

Next we find {{{D[y]}}}.

D<sub>y</sub> has all the same elements as D except that the 2nd column is replaced by
the three numbers that occur after the equal signs in the system, in the
order that they occur top to bottom:

{{{D[y]=abs(matrix(3,3,5,70,0,5,270,25,0,300,25))}}}.

It has value {{{D[y]=-12500}}}.

Next we find {{{D[z]}}}.

D<sub>z</sub> has all the same elements as D except that the 3rd column is replaced by
the three numbers that occur after the equal signs in the system, in the
order that they occur top to bottom:

{{{D[z]=abs(matrix(3,3,5,10,70,5,0,270,0,10,300))}}}..

It has value {{{D[z]=-25000}}}.

The values for x, y, and z are:

{{{matrix(3,1,

matrix(1,7,x,""="",D[x]/D[""],""="", (-10000)/(-2500),""="",4),
matrix(1,7,y,""="",D[y]/D[""],""="", (-12500)/(-2500),""="",5),
matrix(1,7,z,""="",D[z]/D[""],""="", (-25000)/(-2500),""="",10)



)}}}

If you don't know how to find the value of a 3×3 determinant,
go here:

https://www.youtube.com/watch?v=V3e7m-qFDFU 

Edwin</pre></font>