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Question #a9fdf

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Answer 1 · 2016-11-06T21:23:20

$(2, 3) or (3, 2)$ $(2,3)" or " (3,2)$

Explanation:

Rearrange x + 5y in terms of x or y and substitute into xy = 6.

$x + y = 5 \Rightarrow y = 5 - x$ $x+y=5rArry=5-x$

substitute this into xy = 6

$\Rightarrow x (5 - x) = 6$ $rArrx(5-x)=6$

distribute and equate to zero.

$\Rightarrow 5 x - x^{2} = 6 \Rightarrow x^{2} - 5 x + 6 = 0$ $rArr5x-x^2=6rArrx^2-5x+6=0$

Factorising the quadratic gives.

$(x - 2) (x - 3) = 0 \Rightarrow x = 2, x = 3$ $(x-2)(x-3)=0rArrx=2,x=3$

$x = 2 \to y = 5 - 2 = 3 \to (2, 3) is a solution$ $x=2toy=5-2=3to(2,3)" is a solution"$

$x = 3 \to y = 5 - 3 = 2 \to (3, 2) is also a solution$ $x=3toy=5-3=2to(3,2)" is also a solution"$

This can be checked fairly ' easily' as follows.

$x = 2, y = 3 \Rightarrow x + y = 2 + 3 = 5 and x y = 2 \times 3 = 6$ $x=2,y=3rArrx+y=2+3=5" and " xy=2xx3=6$

$x = 3, y = 2 \Rightarrow x + y = 3 + 2 = 5 and x y = 3 \times 2 = 6$ $x=3,y=2rArrx+y=3+2=5" and " xy=3xx2=6$

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