Substitution method Algebra

Question

Solve each system of three equations by substitution method.  I am having trouble with substituting 3 equations with 3 different variables .

 

(3x+y =10),  (4x-z =7) ,  (7y+2z = 17 ) 

Answer 1

3x+y=10

4x-z=7

7y+2z=17

from eq1, y=10-3x

from eq2, z=4x-7

substitute into eq3

7(10-3x)+2(4x-7)=17

70-21x+8x-14=17

56-13x=17

56-17=13x

39=13x

x=39/13

x=3

3x+y=10, 9+y=10, y=1

4x-z=7, 12-z=7, z=5

x=3, y=1, z=5