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Step-by-step explanation:
i) 3x = 4y + 16
2x = 10 + 3y
Shifting places,
3x - 4y = 16 --- (i)
2x - 3y = 10 --- (ii)
We have to use the method of elimination.
So let us eliminate x first.
Multiplying (i) with 2 and (ii) with 3, we get,
2 ( 3x - 4y ) = 16 × 2
6x - 8y = 32 --- (iii)
3 ( 2x - 3y ) = 10 × 3
6x - 9y = 30 --- (iv)
Changing symbols,
6x - 8y = 32
-6x + 9y = -30
x gets eliminated and we remain with,
y = 2
Substituting y = 2 in (i), we get,
3x - 4y = 16
3x - 4 × 2 = 16
3x - 8 = 16
3x = 8
x = 8 / 3
∴ x = 8 / 3 and y = 2
(ii) Given : a,b,c are in continued proportion.
Therefore,
a / b = b / c = c / a
⇒ b² = ac
c² = ab
a² = bc
First, we will look at the LHS.
a / a + 2b = a - 2b / a - 4c
Cross multiplying,
a ( a - 4c ) = ( a - 2b ) ( a + 2b )
a² - 4ac = a² - 4b²
4ac = 4ac ( ∵ b² = ac )
0 = 0
∴ LHS = RHS
Hence, Proved.