SOLUTION: I need help with this following equation : 3x - 7y = 2 2x - 3y = 3 I can only use substitution, please help

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Question 1036672: I need help with this following equation :
3x - 7y = 2
2x - 3y = 3
I can only use substitution, please help

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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I need help with this following equation :
3x - 7y = 2
2x - 3y = 3
I can only use substitution, please help
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3x - 7y = 2,   (1)
2x - 3y = 3.   (2)

Express x from (2):  x = %283+%2B+3y%29%2F2. 

Now substitute ("plug-in") it into equation (1). You will get

3%2A%283%2B3y%29%2F2+-+7y = 2.    (3)

instead of (1). Multiply both sides of (3) by 2 to rid of denominator. You will get

3*(3+3y) - 14y = 4.

Simplify it step by step:

9 + 9y - 14y = 4,

9y - 14y = 4 - 9,

-5y = -5,

y = 1.

Then  x = %283+%2B+3y%29%2F2 = 3.

Answer.  x = 3,  y = 1.

On the Substitution method, Elimination method, Determinants' method for solving the systems of two linear equations in two unknowns see the lessons
    - Solution of the linear system of two equations in two unknowns using determinant
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.