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]