Question

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

Answer 1

The given system of equations is:
2x + 3y = 11 ...................(1)
2x – 4y = – 24 ...................(2)

From equation (1), express x in terms of y:
x = \(\frac{11-3y}{2 }\) ........................(3)

Substitute equation (3) into equation (2):
2(\(\frac{11-3y}{2 }\)) - 4y = -24
11 - 3y - 4y = -24
-7y = -35
y = 5

Substitute the value of y back into equation (3):
x = \(\frac{11-3\times 5}{2}\) = \(\frac{11-15}{2}\) = \(\frac{-4}{2}\) = -2

Therefore, the solution is x = −2 and y = 5.

Given the line equation y = mx + 3, substitute the values of x and y to find m:
5 = m(-2) + 3
5 = -2m + 3
-2m = 5 - 3
-2m = 2
m = -1