Question 652103

They want you to make the 1 a pivot element, meaning that the other numbers in it's column are zero. All you do is use row reduction techniques to accomplish this. 

Divide row {{{2}}} by {{{5}}}
|1| 	5| 	-10| 	0|
|0| 	1| 	-6/5| 	-6/5|
|0| 	10| 	8| 	-5|


Add ({{{-10 * row2}}}) to row{{{3}}}

|1| 	5| 	-10| 	0|
|0| 	1| 	-6/5| 	-6/5|
|0| 	0| 	20| 	7|


Divide {{{row3}}} by {{{20}}}

|1| 	5| 	-10| 	0|
|0| 	1| 	-6/5| 	-6/5|
|0| 	0| 	1| 	7/20|


Add ({{{6/5 * row3}}}) to {{{row2}}}

|1| 	5| 	-10| 	0|
|0| 	1| 	0| 	-39/50|
|0 |	0| 	1| 	7/20|

 
Add ({{{10 * row3}}}) to {{{row1}}}

|1| 	5 |	0| 	7/2|
|0| 	1| 	0| 	-39/50|
|0| 	0| 	1| 	7/20|


Add ({{{-5 * row2}}}) to {{{row1}}}

|1| 	0| 	0| 	37/5|
|0| 	1| 	0| 	-39/50|
|0| 	0| 	1| 	7/20|

so, your solutions are: {{{x= 37/5}}}, {{{y= -39/50}}}, and {{{z= 7/20}}}