SOLUTION: Solve the following linear equations using the Elimination method and The Substitution method 1) X + 3 Y = 2 2X + 5 Y = 3 2) 3X + 4 Y = 12

First system is good to apply the Substitution method.

    X + 3Y = 2      (1)
   2X + 5Y = 3      (2)


From equation (1), express  X = -3Y + 2.  Then substitute it into equation (2),  replacing X there.  
You will get then

    2*(-3Y + 2) + 5Y = 3    (3)


It is equation for one single unknown Y. Simplify it step by step and find Y

    -6Y + 4 + 5Y = 3

    -Y           = 3 - 4 

     -Y          = -1

      Y          = 1.


Now substitute the found value  Y = 1  into equation (1)  to find X.


    X + 3*1 = 2,

or

    X + 3 = 2,

    X     = 2 - 3 = -1.


ANSWER.  The solution is  X= -1,  Y = 1.