Solve the system of linear equations and check any solutions algebraically.

EQ1:  

EQ2:  

EQ3:  

To solve this system of equations, let's use elimination method. In elimination method,  a variable or variables should be eliminated to get the value of the other variable.

Let's eliminate y by multiply EQ3 by -5. Then add it with EQ1.

EQ1:

EQ3:

             

 

                   ...

EQ1:  

EQ2:  

EQ3:  

To solve this system of equations, let's use elimination method. In elimination method,  a variable or variables should be eliminated to get the value of the other variable.

Let's eliminate y by multiply EQ3 by -5. Then add it with EQ1.

EQ1:

EQ3:

             

 

                      Let this be EQ4.         

Eliminate y again by multiplying EQ3 by -2. And add it with EQ2.

EQ2:

EQ3:

              

      

                   

                               Let this be EQ5.

Then, consider two new equations.

EQ4:  

EQ5:

Eliminate the z in these two equations by multiplying EQ5 with 10. And,  add them.

     

     

                     

Then, isolate the x.

Plug-in this value of x to either EQ4 or EQ5.

EQ5:

And, solve for z.

Then, plug-in the values of x and z to either of the original equations.

EQ3:

To check, plug-in the values of x, y and z to the three original equations. If the resulting conditions are all true, then, it verifies it is the solution of the given system of equations.

EQ1:

   

EQ2:

     

EQ3:

   

Therefore, the solution is   .