Question 1175220
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There are many methods -- elimination, Cramer's rule, matrices with Gauss-Jordan....<br>
Using Cramer's rule is a well-defined process; if you want to solve the problem that way, just do it.<br>
Using Gauss-Jordan elimination is also a well-defined process, but there are multiple possible paths to the solution, and the process is prone to simple arithmetic errors.<br>
Given no instruction on what method to use, I would solve the problem algebraically using elimination.<br>
Since one of the equations involves only two of the three variables, I would solve that equation for one variable in terms of the other and then use substitution to reduce the problem to two equations in two unknowns.<br>
Presumably if you are working on a problem like this you know how to solve a system of two linear equations; so I leave the last part of the work to you.<br>
{{{y+2z = -5}}}
{{{y = -5-2z}}}<br>
Then<br>
{{{x-2(-5-2z)+z = -3}}}
{{{x+5z = -13}}}  [1]<br>
and<br>
{{{x+(-5-2z)+3z = -6}}}
{{{x+z = -1}}}  [2]<br>
Solve [1] and [2] for x and z; then find y from one of the given equations.<br>