# solve for x and y

label Algebra
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x+y=26;  xy=153.  solve for x & y?

Oct 28th, 2015

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x + y = 26 ---(1)

xy = 153 ---(2)

From equation (1)

y = 26 - x ---(3)

Substitute y from equation (3) in equation (2)

x(26 - x) = 153

$\\ 26x-x^2=153\\ \\ -x^2+26x-153=0\\ \\ Multiply\hspace{5}both\hspace{5}sides\hspace{5}by\hspace{5}-1\\ \\ x^2-26x+153=0\\ \\ Now\hspace{5}factorise\hspace{5}by\hspace{5}splitting\hspace{5}the\hspace{5}middle\hspace{5}term\\ \\ x^2-17x-9x+153=0\\ \\ x(x-17)-9(x-17)=0\\ \\ (x-17)(x-9)=0\\ \\ x-17=0\hspace{5}or\hspace{5}x-9=0\\ \\ x=17\hspace{5}or\hspace{5}x=9\\$

Substitute x=17 in equation (3)

y = 26 - 17 = 9

Substitute x=9 in equation (3)

y = 26 - 9 = 17

So the solution is (17, 9) and (9, 17).

These are the points at which the line and the curve intersect.

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Oct 28th, 2015

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Oct 28th, 2015
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Oct 28th, 2015
Nov 24th, 2017
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