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 = ...........(3) Substituting above value of x in equation (2), we get : Substituting value of y in equation (3), we get : Substituting value of x and y in y = mx + 3, we get : ⇒ 5 = -2m + 3 ⇒ -2m = 5 - 3 ⇒ -2m = 2 ⇒ m = = -1. Hence, x = -2, y = 5 and m = -1.