L O.

asked • 03/08/14

solving systems of equations

did I solve this correctly?
  3x + y = 7
  3x + y = 10  (mulitply by -1)
=   -1(3x + y) = -1(10)
=    -3x -y = -10
=    3x + y = 7
     -3x -  y = = -10
                 = -3
I said it cannot be solved because you are eliminating both x and y from the equation

2 Answers By Expert Tutors


Kay G. answered • 03/08/14

4.9 (34)

~20 Years Accounting Tutoring Experience

L O.

woud I answer it as a solution and call it infinity?


Kyle M.

Kay is saying that there is no solution, but eliminating x & y is not the reason.
Think about it:
Try substitution: 7=10
There can be no solution. The reason is that there are no values x & y which will yield both 7 & 10. It is simply impossible.


Kay G.

Sorry, didn't mean to confuse you.
As Kyle said, there's no solution (you were correct on that point), but it's not because x & y were eliminated (so you were incorrect on that point).  It's important that you don't drop the 0 off the left side, and important you understand the reason.
You can have 2 situations where x and y disappear like that:
1) If what you're left with is incorrect (such as 0 = -3), then there's no solution. Remember a "solution" is what makes the equation true, and with two equations, it must be true for both, i.e. they have to cross somewhere.  No solution means no crossing and you have parallel lines.
2) If what you're left with is correct (such as 0 = 0) then it's all solutions, infinity, dependent, equivalent, whatever your book is calling it.  This means that all points are solutions for both equations, hence, they are on top of each other, sharing all the points in common.


Steve S.

"all points are solutions for both equations", meaning, "all points on the line are solutions for both equations".


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