SOLUTION: I need detail solution: If {{{x/5 + y/2 = 5}}} and {{{ x^2+y^2=164 }}}, find the value of A = {{{sqrt(x^2

SOLUTION: I need detail solution: If {{{x/5 + y/2 = 5}}} and {{{ x^2+y^2=164 }}}, find the value of A = {{{sqrt(x^2 - y^2)}}}

Question 823879: I need detail solution:
If and , find the value of A =
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Solve for either x or y in the linear equation and substitute into the quadratic equation; and solve for the single variable found there. You may have two solutions for this variable. Use the linear equation to find the value of the other variable. You can then compute A according to its given formula.

Please find the steps you need according to my solution description. You should hopefully not have any significant trouble.

------------------------------------------------------------------
In case of difficulty, a beginning.
The linear equation gives you ;
Substituting,
.

.
and further simplifying,
.

If you follow the general solution to quadratic formula and simplifying, you will obtain that x
, note that this is two values for x, so you use the linear equation to find the corresponding two values for y.

--------------
Continuing
--------------

1771 is not further simplifiable. The solutions, decimalized, for x are
or ;
and substituting for each of those in , find that
or .

Solution points, (x,y) are therefore: (-20.833, 4.5833) and (12.7475, 1.22525).

You can now compute A.
RELATED QUESTIONS
I need more detail solution and explanation: If 3x+y-2z=7 and x-y-2z=5, find the value... (answered by richwmiller)

FInd x and y in the following: a) 6+sqrt{x-y}=x+y+3sqrt{2} b) xy+sqrt{x+y}= (5/4) +... (answered by josgarithmetic)

Find the smallest possible value: {{{sqrt(x^2+y^2)}}} + {{{sqrt((x-1)^2+y^2)}}} +... (answered by ikleyn)

Let x and y be real numbers. Find the maximum value of (x + y)^2, if x and y satisfy x^2 (answered by CPhill,ikleyn,Edwin McCravy)

I need mire detail solution (and explanation what formulas should be used): The two... (answered by Alan3354)

I need help please. if x=yz,find the value for x given that y=2 and... (answered by tutorcecilia)

Find the value of 2^x+2 + 2^x= 5^y+1 -... (answered by Alan3354,greenestamps)

If x + y = 11 and y = 15/x, find the value of x^2 +... (answered by Edwin McCravy,jim_thompson5910)

What is the solution to the system of equations x^2 - x + 6 = y and 2x + 2y = 36?... (answered by jim_thompson5910)