Find the sol ution of the given system of equations. x + y − 8 2 = x + 2 y − 14 8 = 3 x + y − 12 11 Options: A . &nbsp (1, -1) B . &nbsp (2, 6) C . &nbsp (2, 2) D . &nbsp (0, 1)

Answer: Option B : B Take first two components, x + y − 8 2 = x + 2 y − 14 8 ⇒ 8 ( x + y − 8 ) = 2 ( x + 2 y − 14 ) ⇒ 8 x + 8 y − 64 = 2 x + 4 y − 28 ⇒ 6 x + 4 y − 36 = 0 ⇒ 3 x + 2 y − 18 = 0 . . . . . ( i ) Take last two components, x + 2 y − 14 8 = 3 x + y − 12 11 ⇒ 11 ( x + 2 y − 14 ) = 8 ( 3 x + y − 12 ) ⇒ 11 x + 22 y − 154 = 24 x + 8 y − 96 ⇒ − 13 x + 14 y − 58 = 0 . . . . . ( i i ) On multiplying equation ( i ) by 7, we get ⇒ 21 x + 14 y − 126 = 0... ( i i i ) , On subtracting equation (ii) from (iii), we get ⇒ 34 x = 68 ⇒ x = 2 On substituting value of x = 2 in equation ( i ) , we get 3 × 2 + 2 y − 18 = 0 ⇒ y = 6 ∴ The solution is (2, 6).

Find the solution of the given system of equations. x+y−82=x+2y−

Question

Find the solution of the given system of equations.

$\frac{x + y - 8}{2} = \frac{x + 2 y - 14}{8} = \frac{3 x + y - 12}{11}$

Options:

A . (1, -1)

B . (2, 6)

C . (2, 2)

D . (0, 1)

Answer: Option B
:
B

Take first two components,
$\frac{x + y - 8}{2} = \frac{x + 2 y - 14}{8}$
$\Rightarrow 8 (x + y - 8) = 2 (x + 2 y - 14)$
$\Rightarrow 8 x + 8 y - 64 = 2 x + 4 y - 28$
$\Rightarrow 6 x + 4 y - 36 = 0$
$\Rightarrow 3 x + 2 y - 18 = 0 . . . . . (i)$

Take last two components,
$\frac{x + 2 y - 14}{8} = \frac{3 x + y - 12}{11}$
$\Rightarrow 11 (x + 2 y - 14) = 8 (3 x + y - 12)$
$\Rightarrow 11 x + 22 y - 154 = 24 x + 8 y - 96$
$\Rightarrow - 13 x + 14 y - 58 = 0 . . . . . (i i)$

On multiplying equation $(i)$ by 7, we get
$\Rightarrow 21 x + 14 y - 126 = 0... (i i i)$ ,
On subtracting equation (ii) from (iii), we get
$\Rightarrow 34 x = 68$
$\Rightarrow x = 2$
On substituting value of $x = 2$ in equation $(i)$ , we get
$3 \times 2 + 2 y - 18 = 0$
$\Rightarrow y = 6$
$∴$ The solution is (2, 6).