Question

Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordered pair.
Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair.

x - 2y = 0 
5x + 2y = 24

Answer 1

Substitution:

Step 1: Choose one of the two equations and solve for either x or y.

     x - 2y = 0
       + 2y  +2y
--------------------------
     x = 2y + 0 

Step 2: Plug in the value you got for x or y into the equation you did not work with in Step 1.

5(2y + 0) + 2y = 24
10y + 0 + 2y = 24
 
12y = 24
------- ------
  12    12

y = 2 

Step 3: Plug in the number you got for y into either equation.

     5x + 2(2) = 24
     5x + 4 = 24
          - 4    - 4
---------------------------
     5x = 20
   ------ ------
      5      5

x = 4

Your final answer should be written as a coordinate pair: (4,2).
____________________________________________________________

Elimination:

Add the two equations together to eliminate y.

     x - 2y = 0
+ 5x + 2y = 24
----------------------
   6x = 24
 ------ ------
    6      6

x = 4

Step 2: Substitute the x value into the original equation to find y.

5(4) + 2y = 24       20 + 2y = 24
                           - 20          - 20
                       --------------------------
                             2y = 4 
                           ------ -----
                              2     2
  
                             y = 2

I hope this answer helps you :D