SOLUTION: Hello. This a problem I am having trouble with in my lesson called the "Addition Method". I have to find the solution to the system of equations or, in other words, the ordered pai

Question 435297: Hello. This a problem I am having trouble with in my lesson called the "Addition Method". I have to find the solution to the system of equations or, in other words, the ordered pair that results from solving and substituting. I'm sure you already understand that though. :) Thanks in advance. (It is a multiple choice question so the 3 options are below where it says "The solution to the system of equations is _____.")
7x - 3y = 4
2x - 4y = 1
The solution to the system of equations is _____.
--(13/34, -15/34)
--(3/22, -7/22)
--(13/22, 1/22)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
7x - 3y = 4
2x - 4y = 1
---------------
Note: Substitution is not the best way to
solve this system
of equations.
---------------
However:
Solve the 2nd equation for "y":
4y = 2x-1
y = (2x-1)/4
---
Substitute that into the 1st equation and solve for "x":
---
7x -(3/4)(2x-1) = 4
28x -3(2x-1) = 16
28x-6x+3 = 16
22x = 13
x = 13/22
--------------------
So I guess (13/22, 1/22) is the correct answer.
Let's see.
---
Substitute for "x" in the 1nd equation and solve for "y":
7x - 3y = 4
7(13/22) - 3y = 4
3y = (91/22)-(88/22)
3y = 3/22
y = 1/22
================
OK
======================
Cheers,
Stan H.
===========================

The solution to the system of equations is _____.
--(13/34, -15/34)
--(3/22, -7/22)
--(13/22, 1/22)
---------------------

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