Answer to Question 1

Remember:  In mathematics there are often many acceptable solutions to a problem.  These answers show you "possible" solutions.  While the final answers are always the same, the methods of arriving at the answers may differ.

1.
Solution by Addition or Subtraction Solution by Substitution
x + y = 1
x + 3y = 9   

  x + y = 1    subtract
-x -3y = -9

   -2y = -8

      y = 4   answer for y

x + 4 = 1   substitute to get answer for x
x = -3

 

check:

x + y = 1
x + 3y = 9   

y = 1 -   solve first equation for "y="

x + 3(1 - x) = 9   substitute into the second 

x + 3 - 3x = 9
-2x + 3 = 9
-2x = 6
x = -3  
answer for x

x + y = 1  substitute to get answer for y
-3 + y = 1
y = 4

check:

x + y = 1
-3 + 4 = 1
1 = 1 check!
x + 3y = 9 
-3 + 3(4) = 9
-3 + 12 = 9
9 = 9 check!  
x + y = 1
-3 + 4 = 1
1 = 1 check!
x + 3y = 9 
-3 + 3(4) = 9
-3 + 12 = 9
9 = 9 check!