Question

solve using substitution method 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of 'm' for which y = mx + 3

Answer 1

2x + 3y = 11 .......(i)
2x - 4y = -24......(ii)

solving these equations by substitution method, 
Now, from (ii), we get, 

2x-4y=-24
2x=-24+4y
x=(-24+4y)/2
x=-24/2+4y/2
x=-12+2y...........(iii)

Put this value of x in (i), we get, 

 2(-12+2y) + 3y = 11
-24+4y+3y=11
7y=11+24
7y=35
y=35/7
y=5

now put this value of y in (iii)

=-12+2y
=-12+2(5)
=-12+10
=-2

y=mx+3                                      {y=5,x=-2)
5=m(-2)+3
5=-2m+3
5-3=-2m
2=-2m
2/2=-m
1=-m
-1=m

Answer 2

2x + 3y = 11 ------(1)
2x - 4y = -24--------(2)

From equation (2),we get
2x-4y=-24
2(x-2y)=2(-12)
x-2y=-12
x=-12+2y

Put x=-12+2y in equation (1)

2x + 3y = 11
2(-12+2y)+3y=11
-24+4y+3y=11
7y=11+24
7y=35
y=35/7
y=5

x=-12+2y
x=-12+2(5)
x=-12+10
x=-2

y=mx+3
5=m(-2)+3
5=-2m+3
-2m=5-3
-2m=2
m=2/-2
m=-1

Hope it helps