SOLUTION: ​ 21x+7y=42 −5x+5y=10 ​ what would x and y be? I am not sure how to solve these problems if the equations don't equal y.

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Question 1189285: ​

21x+7y=42
−5x+5y=10
​
what would x and y be? I am not sure how to solve these problems if the equations don't equal y.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
21x+7y=42
−5x+5y=10
​
what would x and y be? I am not sure how to solve these problems if the equations don't equal y.
~~~~~~~~~~~~~~~ 

Your starting equations are

    21x + 7y = 42      (1)

    −5x + 5y = 10      (2)


In the first equation, divide both sides by 7.

In the second equation, divide both sides by 5. You will get an EQUIVALENT system of equations

    3x + y = 6        (3)

    -x + y = 2.       (4)


From equation (3), subtract equation (4). You will get then, after canceling the terms with "y"

    3x - (-x) = 6 - 2

       4x     =   4

        x     =   4/4 = 1.


Next, substitute x= 1 into equation (4).  You will get

    -1 + y = 2,

or       y = 2 + 1 = 3.


ANSWER.  The solution to the given system opf equations is  x= 1,  y= 3.


CHECK.   Check it ON YOUR OWN, that the found values x= 1, y= 3 satisfy the given equations (1) and (2).

Solved and explained.


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As I see from your post, the level of your knowledge is about zero on this subject.


On solving systems of linear equations, see the lessons
    - 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
in this site.