Question

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

Answer 1

Answer:

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

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Answer 2

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2x + 3y = 11…………………………..(i)

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

From equation (ii), we get;

x = (11 – 3y)/2 ……….…………………………..(iii)

Putting the value of x in equation (ii), we get

2[(11 – 3y)/2] – 4y = −24

11 – 3y – 4y = -24

-7y = -35

y = 5……………………………………..(iv)

Putting the value of y in equation (iii), we get;

x = (11 – 15)/2 = -4/2 = −2

Hence, x = -2, y = 5

Also,

y = mx + 3

5 = -2m +3

-2m = 2

m = -1

Therefore, the value of m is -1

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