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.