Question

Solve 2x + 3y = 11 and 2x – 4y = -24 and hence find the value of m for

which y = mx + 3​

Answer 1

Answer:

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Given pair of liner equation is

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

and 2x-4y = -24 --(2)

From (2)

2x =4y-24

or. 2x = 2( 2y- 12)

x = 2y - 12 --(3)

Substitute this value of x in (1) we get,

2(2y-12) +3y =11

or 4y-24+3y=11

or 7y = 11+24

7y= 35

or. y= 35/7

y= 5

Substitute this value of y in (3) we get,

x= 2(5)-12

= 10-12

= -2

Now consider y= mx+3

Substitute the value of x=-2,y= 5 we get,

5=m (-2) + 3

or. 5-3= -2m

or. 2= -2m

or. -2m= 2

or. m= 2/-2

m= -1

Hence,. x= -2, y= 5 and m= -1 Ans

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Answer 2

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2x + 3y = 11………………..(I)

2x – 4y = -24………………… (II)

From equation (II), we get

x = (11-3y)/2 ………….(III)

Substituting 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 = (11-3×5)/2 = -4/2 = -2

Hence, x = -2, y = 5

Also,

y = mx + 3

5 = -2m +3

-2m = 2

m = -1