Can you give me some advice for solving these math problems (solving systems of equations in three variables)?

a + b = 3


-b + c = 3


a + 2c = 10





and





p + 4r = -7


p - 3q = -8


q + r = 1





any help is appreciated!!Can you give me some advice for solving these math problems (solving systems of equations in three variables)?
Let's start with the first set of equations.





I. a + b = 3


II. -b + c = 3


III. a + 2c = 10





Take equation I. and find a:


I. a + b = 3


** a = 3 - b **





Take equation II. and find c:


II. -b + c = 3


** c = 3 + b **





Plug the two ** equations above into equation III:


III. a + 2c = 10


(3 - b) + 2(3 + b) = 10


3 - b + 6 + 2b = 10


9 + b = 10


b = 1





Plug b = 1 into the equations I. and II. to find a and c:


I. a + b = 3


a + 1 = 3


a = 2





II. -b + c = 3


-1 + c = 3


c = 4





So, a = 2, b = 1, c = 4.








Now let's do the second set of equations.





I. p + 4r = -7


II. p - 3q = -8


III. q + r = 1





Take equation II. and find p:


II. p - 3q = -8


** p = -8 + 3q **





Take equation III. and find r:


III. q + r = 1


** r = 1 - q **





Plug the two ** equations above into equation I:


I. p + 4r = -7


(-8 + 3q) + 4(1 - q) = -7


-8 + 3q + 4 - 4q = -7


-4 - q = -7


3 = q





Plug 3 = q into the equations II. and III. to find p and r:


II. p - 3q = -8


p - 3(3) = -8


p - 9 = -8


p = 1





III. q + r = 1


3 + r = 1


r = -2





So, p = 1, q = 3, r = -2.