Homework Help

How do I figure out the following: If xy=546 and x+y=26, then what are x and y?

user profile pic

callayne | Student, Undergraduate | eNotes Newbie

Posted November 20, 2011 at 6:35 AM via web

dislike 0 like

How do I figure out the following:

If xy=546 and x+y=26, then what are x and y?

4 Answers | Add Yours

user profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted November 20, 2011 at 6:46 AM (Answer #1)

dislike 0 like

The easiest way is to graph both equations and locate the point(s) of intersection.  In this case, there are no points of intersection.  Therefore, this has no solution.

user profile pic

gs01 | Student, Undergraduate | eNoter

Posted November 20, 2011 at 7:08 AM (Answer #2)

dislike 0 like

Since x+y = 26 ...........(1),

 and xy = 546.............(2)

x = 26-y

therefore substituting the value of x in equation 2

(26-y)y = 546

26Y - y^2 = 546  Taking all the numbers on the right side

Y^2 -26Y +546 = 0

Since it is a quadratic or 2nd degree eauation we will have two values for Y using equation for ax^2+ bx+c =

 

(b+and -(Sqrt(b^2-4ac)/2a)

-26+Sqrt(26^2-4*1*546)/2*1) and -26-Sqrt(26^2-4*1*546)/2*1)

 Y= 13 + 19.41648783i or Y= 13 - 19.41648783i

i = sqrt (-1) is called the imaginary part.

and x = 26-Y

 

user profile pic

callayne | Student, Undergraduate | eNotes Newbie

Posted November 20, 2011 at 7:27 AM (Answer #3)

dislike 0 like

Thanks for the help, people.  The 2nd answer is more advanced than where we are right now.  We're supposed to be using the ac method or, if that doesn't work evenly, then we're supposed to use a factoring method.

user profile pic

atyourservice | TA , Grade 10 | Valedictorian

Posted June 30, 2014 at 12:05 PM (Answer #4)

dislike 0 like

I graphed it since i kept getting confused at my math and there are no real solutions

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes