Solve: x =-4y and (x-y)/10 = (x-6)/2

Solve x =-4y and (x-y)/10 = (x-6)/2 by Substitution and Elimination Method

Substitution Method

x =-4y —(i)

$\frac{x – y}{10} = \frac{x – 6}{2}$ —(ii)

Substituting the value of x in equation (ii) we get,

$\frac{x – y}{10} = \frac{x – 6}{2}$

$\Rightarrow \frac{ – 4y – y}{10} = \frac{ – 4y – 6}{2}$

$\Rightarrow \frac{ – 5y}{10} = \frac{ – 4y – 6}{2}$

$\Rightarrow \frac{ – y}{2} = \frac{ – 4y – 6}{2}$

$\Rightarrow – y = – 4y – 6$

$\Rightarrow 4y – y = – 6$

$\Rightarrow 3y = – 6$

$\Rightarrow y = \frac{ – 6}{3}$

$\Rightarrow y = – 2$

From equation (i) we get,

x=-4y =-4(-2) =8

Required Solutions are x = 8 , y = -2 [Ans]

Elimination Method

x =-4y —(i)

$\frac{x – y}{10} = \frac{x – 6}{2}$ —(ii)

From Equation (i) we get,

x+4y=0 —(iii)

From equation (ii) we get,

$\frac{x – y}{10} = \frac{x – 6}{2}$

⇒ 2(x-y)=10(x-6)

⇒ 2x-2y = 10x -60

⇒ 2x-2y-10x=-60

⇒ -8x-2y=-60

⇒ -2(4x+y) = -60

⇒ 4x+y = $\frac{ – 60}{ – 2}$

⇒ 4x+y = 30 —(iv)

Multiplying Equation (iii) by 4 we get,

4x+16y=0 —-(v)

Subtracting (v) from (iv) we get,

(4x+y)-(4x+16y) = 30

⇒ 4x+ y -4x -16y = 30

⇒ -15y = 30

⇒ y = $\frac{30}{ – 15}$

⇒ y = -2

From (i) we get,

x = -4y =-4(-2) = 8

Required Solutions are x = 8 , y = -2 [Ans]

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