Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.

Given,

2x + 3y = 11 ……….(1)

2x - 4y = -24 ………(2)

Solving equation (1), we get :

⇒ 2x + 3y = 11

⇒ 2x = 11 - 3y

⇒ x = $\dfrac{11 - 3y}{2}$ ………..(3)

Substituting above value of x in equation (2), we get :

$\Rightarrow 2 \times \Big(\dfrac{11 - 3y}{2}\Big) - 4y = -24 \\[1em] \Rightarrow 11 - 3y - 4y = -24 \\[1em] \Rightarrow 11 - 7y = -24 \\[1em] \Rightarrow 7y = 11 + 24 \\[1em] \Rightarrow 7y = 35 \\[1em] \Rightarrow y = \dfrac{35}{7} = 5.$

Substituting value of y in equation (3), we get :

$\Rightarrow x = \dfrac{11 - 3 \times 5}{2} \\[1em] \Rightarrow x = \dfrac{11 - 15}{2} \\[1em] \Rightarrow x = \dfrac{-4}{2} = -2.$

Substituting value of x and y in y = mx + 3, we get :

⇒ 5 = -2m + 3

⇒ -2m = 5 - 3

⇒ -2m = 2

⇒ m = $\dfrac{2}{-2}$ = -1.

Hence, x = -2, y = 5 and m = -1.