Question 819366
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Hi
{{{4x[1]-x[2]+2x[3]=3}}}
{{{-4x[1]+x[2]-3x[3]=-10}}}  |Adding first 2 EQ, {{{x[3] = 7}}}
{{{8x[1]-2x[2]+9x[3]=-1 }}}  |Multiplying 2nd EQ by 2 and adding to 3rd EQ{{{x[3] = -7}}}
 7 &#8800;  -7   no solution                                                  
 Basic Plan:
•	Use a pair of equations and eliminate one variable.
•	Use a different pair of equations and eliminate the same variable.
•	Solve the two-variable system found, determining the values of those variables.
•	Substitute those into an original equation to find the remaining variable’s value.

Note: A false statement generated ( &#8800; ) indicates no solution                                                    
A true statement (an identity) signals infinitely many solutions.