Solve `2x+3y=11 and x-2y= -12 ` algebraically and hence find the value of 'm' for which `y= mx+3`.

Explanation

`2x+ 3y = 11" "...(1)`
`x- 2y = -12" "...(2)`
(2) `rArr x = 2y - 12" "...(3)`
Substitute value of x from (3) in (1), we get
`2 (2y- 12) + 3y= 11`
`rArr 4y - 24 + 3y= 11`
`rArr 7y = 35`
`rArr y = 5`
Subtituting value of `y=5` in equation (3), we get
`x = 2(5) -12 = 10 - 12 = -2`
Hence `x= -2, y=5` is the required solution
Now `5= -2m +3`
`rArr 2m = 3-5`
`rArr 2m = -2`
`m= -1`