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)}}}

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Question 823879: I need detail solution:
If x%2F5+%2B+y%2F2+=+5 and +x%5E2%2By%5E2=164+, find the value of A = sqrt%28x%5E2+-+y%5E2%29
Answer by josgarithmetic(39617) About Me  (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.



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In case of difficulty, a beginning.
The linear equation gives you y=-x%2F10%2B5%2F2;
Substituting, x%5E2%2B%28-x%2F10%2B5%2F2%29%5E2=164
.
x%5E2%2B%281%2F100%29%2825-x%29%5E2=164
.
and further simplifying,
.
101x%5E2-50x-15775=0
If you follow the general solution to quadratic formula and simplifying, you will obtain that x
x=%2825%2B-+30%2Asqrt%281771%29%29%2F%28101%29, note that this is two values for x, so you use the linear equation to find the corresponding two values for y.

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Continuing
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1771 is not further simplifiable. The solutions, decimalized, for x are
x=-20.833 or x=12.7475;
and substituting for each of those in y=-x%2F10%2B5%2F2, find that
y=4.5833 or y=1.22525.

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

You can now compute A.