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

Explanation

We have, 2x + 3y = 11 …(1)
and 2x - 4y = - 24 …(2)
From equation (2), 4y = 2x + 24
or `y = (x + 12)/(2)` …(3)
On substituting y from equation (3) in (1), we get
2x + 3 `((x + 12)/(2)) = 11`
`implies 4x + 3 (x + 12) = 11 xx 2`
implies 4x + 3x + 36 = 22
implies 7x = 22 - 36
implies 7x = - 14
implies x = - 2
On substituting x = - 2 in equation (3), we get
`y = (-2+12)/(2) implies y = (10)/(2) = 5`
On substituting x = - 2 and y = 5 in the equation y = mx + 3, we get
5 = m `xx` (-2) + 3
implies 5 = - 2m + 3
implies 2m = 3 - 5 = - 2
implies m = - 1