Solve the following equation for x and y by cross multiplication method
(ax-by)+(a+4b)=0
(bx+ay)+(b-4a)=0
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The given system of equation may be written as
2(ax - by) + a + 4b = 0
So, 2ax - 2by + a + 4b ..............(i)
2(bx + ay) + b - 4a = 0
so, 2bx+2ay+b-4a=0................(ii)
compare (i) and (ii) with standard form, we get
a1 = 2a, b1 = -2b, c1 = a + 4b
a2 = 2b, b2 = 2a, c2 = b - 4a
By cross multiplication method
x−2b2+8ab−2a2−8abx−2b2+8ab−2a2−8ab =−y2ab−8a2−2ab−8b2=−y2ab−8a2−2ab−8b2 =14a2+4b2=14a2+4b2
x−2b2−2a2=−y−8a2−8b2=14a2+4b2x−2b2−2a2=−y−8a2−8b2=14a2+4b2
Now, x−2b2−2a2=14a2+4b2x−2b2−2a2=14a2+4b2
⇒x=−12⇒x=−12
And, −y−8a2−8b2=14a2+4b2−y−8a2−8b2=14a2+4b2
⇒y=2⇒y=2
Therefore, the solution of the given pair of equations are −12−12 and 2 respectively.
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