Question

Solve x + 3y =6 and 2x - 3y = 12 and hence find the value of k for which3y = xk +3.​

Answer 1

To solve:-

x + 3y = 6

2x - 3y = 12

To find:-

The value of k for 3y = xk + 3

Method:-

Substitution method.

Solution:-

$\sf{x+3y = 6 \longrightarrow (i)}$

$\sf{2x-3y = 12 \longrightarrow (ii)}$

From eq.(i),

$\sf{x + 3y = 6}$

$\sf{\implies x = 6 - 3y}$

Substituting the value of x in equation (ii)

$\sf{2x - 3y = 12}$

= $\sf{2\times(6 - 3y) - 3y = 12}$

$\sf{\implies 12 - 6y - 3y = 12}$

$\sf{\implies -9y = 12 - 12}$

$\sf{\implies -9y = 0}$

$\sf{\implies y = \dfrac{0}{-9}}$

$\sf{\implies y = 0}$

Putting the value of y in eq.(i)

$\sf{x + 3y = 6}$

= $\sf{x + 3\times0 = 6}$

$\sf{\implies x+0 = 6}$

$\sf{\implies x = 6}$

Therefore,

Value of x = 6

Value of y = 0

Now,

$\sf{3y = xk + 3 \longrightarrow (iii)}$

Putting the value of x and y in eq.(iii)

$\sf{3y = xk + 3}$

= $\sf{3\times 0 = 3k + 3}$

$\sf{\implies 3k + 3 = 0}$

$\sf{\implies 3k = -3}$

$\sf{\implies k = \dfrac{-3}{3}}$

$\sf{\implies k = -1}$

$\sf{\therefore The\:value\:of\:k\:is\:-1}$