solve the following simultaneous equations:

(i) 3/rootx+4/rooty=17/6 ; 5/rootx-6/rooty=1/2

(ii) 2(3x-y)=5xy ; 2(x=3y)=5xy (x is not equal to 0,y is not equal to 0)

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Question

solve the following simultaneous equations:
(i) 3/rootx+4/rooty=17/6 ; 5/rootx-6/rooty=1/2
(ii) 2(3x-y)=5xy ; 2(x=3y)=5xy (x is not equal to 0,y is not
equal to 0)

brainmasswriter2 · Accepted Answer

Let $\frac{1}{\sqrt{x}} = u a n d \frac{1}{\sqrt{y}} =v$

So the equations can be re-written as :

$3 u + 4 v = \frac{17}{6} ... (1) 5 u - 6 v = \frac{1}{2} ... (2)$

Now we multiply equation(1) with 6 and equation (2) with 4 and add resulting equations and we get:

$38 u = 19 \Rightarrow u = \frac{1}{2} \Rightarrow \frac{1}{\sqrt{x}} = \frac{1}{2} \Rightarrow \sqrt{x} = 2 \Rightarrow x = 4$

Now to get y we multiply equation(1) with 5 and equation (2) with -3 and add the resulting equations to get:

$38 v = \frac{76}{6} \Rightarrow v = \frac{1}{3} \Rightarrow \frac{1}{\sqrt{y}} = \frac{1}{3} \Rightarrow \sqrt{y} = 3 \Rightarrow y = 9$

solve the following simultaneous equations: (i) 3/rootx+4/rooty=17/6 ; 5/rootx-6/rooty=1/2 (ii) 2(3x-y)=5xy ; 2(x=3y)=5xy (x is not equal to 0,y is not equal to 0)

solve the following simultaneous equations:

(i) 3/rootx+4/rooty=17/6 ; 5/rootx-6/rooty=1/2

(ii) 2(3x-y)=5xy ; 2(x=3y)=5xy (x is not equal to 0,y is not equal to 0)