Solve the system of linear equations

Let's do this problem using the method of addition and subtraction.  Mult. the first equation by 5, to obtain 10x  +  0  + 10z = 10.  Mult. the second equation by -2, to obtain -10x  -  6y  +  0  =  -8.

Now add these two equations together.  Variable "x" will disappear, leaving us with -6y  + 10z = 2.  You can divide all terms by 2 to reduce this equation:

-3y + 5z = 1
 3y - 4z  = 4  (This is the third original equation.)

                        Now, use the same approach to solve this system of linear equations in 2 variables.    z=5.

Work backwards now to find y.  Subst. 5 for z in either equation and calculate y.  Finally, subst. your z and y values into any of the 3 original equations to solve for x.