SOLUTION: What is the difference (y-x) if: 6x + 5y + √(6x + 5y) = 72 3x - 4y + √(3x - 4y) = 30

Algebra.Com
Question 1171175: What is the difference (y-x) if:

6x + 5y + √(6x + 5y) = 72
3x - 4y + √(3x - 4y) = 30

Answer by ikleyn(52839)   (Show Source): You can put this solution on YOUR website!
.

            First,  we accept the agreement that we consider only positive values of the square roots.

            After that,  we solve the problem in several steps.


Step 1.  We find 6x + 5y from the first equation.


     = 72.


    For it, we introduce new variable u = .

    Then the equation takes the form

         u^2 + u = 72

         u^2 + u - 72 = 0

         (u+9)*(u-8) = 0.

     The roots are -9 and 8, but we accept only positive root  u= 8.


     Then we have THIS equation 

         6x + 5y = ,   or

         6x + 5y = 64.    (1)


     Step 1 is complete.




Step 2.  We find 3x - 4y from the second equation.


     = 30.


    For it, we introduce new variable v = .

    Then the equation takes the form

         v^2 + v = 30

         v^2 + v - 30 = 0

         (v+6)*(v-5) = 0.

     The roots are -6 and 5, but we accept only positive root  v= 5.


     Then we have THIS equation 

         3x - 5y = ,   or

         3x - 5y = 25.    (2)


     Step 2 is complete.




Step 3.  Solving the system (1), (2) to find x and y.


    The system is

         6x + 5y = 64.    (1)

         3x - 5y = 25.    (2)


    Solve it by ANY WAY you know / (you like) / (you prefer).


    The solution is  x = ;  y = .




Step 4.  Calculate  y - x.


    It is    y - x =  -  =  = -8.


The solution is completed.


The   ANSWER   is   y - x = -8.


        ***************
            SOLVED.
        ***************



RELATED QUESTIONS

Find the difference if (y-x) if {{{6x + 5y + sqrt(6x + 5y) =72}}} and {{{3x - 4y +... (answered by math_tutor2020)
3x + 5y =54 6x + 4y =... (answered by math_helper,ikleyn)
find the solution of x+y 3x+4y=-30... (answered by TimothyLamb)
6x(-5y) + (-3x)(-4y) Simplify and... (answered by jim_thompson5910)
what is the value of x and y if the equation is... (answered by MathLover1)
(9x+4y) (-6x-5y)... (answered by rfer)
simplify & solve 6x(-5y)+(-3x)(-4y) Thank... (answered by vidhyak)
What is the ordered pair(x,y) form 3x + 5y = 21 -9x + 4y =... (answered by mananth)
If 3x+y=24 and 6x+11y=24 what is the value of... (answered by DrBeeee)