Question

(2) solve 2x +3y=11 and 2x - 4y =-24 and hence find the value of 'm' for which y=mx + .3
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Answer 1

Answer:

2x+3y = 11

2x-4y = 24

subtracting them we get

y= -13/7

Now put the value of y in any equation

2x+3* -13/7=11

2x-39/7=11

2x=11+39/7

2x=116/7

x=58/7

Now find the value of m

y = mx +3

-13/7 =m*58/7 + 3

- 13/7 - 3 =58m/7

- 34/7 = 58m/7

7 and 7 get cancelled

Now we get

m = -34/58

m = - 34/58

m = -17/29

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Answer 2

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• $\rm\:2x+3y=11\:..........................(i)$

• $\rm\:2x-4y=-24\:.......................(ii)$

Now,

⪼ From eq (i)

$\rm\:2x+3y=11$

$\rm\longrightarrow\:2x=11-3y$

$\rm\longrightarrow\:x=\dfrac{11-3y}{2}\:.................(iii)$

⪼ Putting the value of x in eq (ii)

$\rm\:2x-4y=-24$

$\rm\longrightarrow\:\cancel{2}\bigg(\dfrac{11-3y}{\cancel{2}}\bigg)-4y=-24$

$\rm\longrightarrow\:11-3y-4y=-24$

$\rm\longrightarrow\:11-7y=-24$

$\rm\longrightarrow\:-7y=-24-11$

$\rm\longrightarrow\:-7y=-35$

$\rm\longrightarrow\:y=\cancel\dfrac{-35}{-7}$

$\rm\longrightarrow\:y=5$

⪼ Putting the value of y in eq (iii)

$\rm\:x=\dfrac{11-3y}{2}$

$\rm\longrightarrow\:x=\dfrac{11-3\times\:5}{2}$

$\rm\longrightarrow\:x=\dfrac{11-15}{2}$

$\rm\longrightarrow\:x=\cancel\dfrac{-4}{2}$

$\rm\longrightarrow\:x=-2$

⪼ According to the question,

$\rm\:y=mx+3$

$\rm\longrightarrow\:5=m\times\:(-2)+3$

$\rm\longrightarrow\:5=-2m+3$

$\rm\longrightarrow\:5-3=-2m$

$\rm\longrightarrow\:2=-2m$

$\rm\longrightarrow\:\cancel\dfrac{-2}{2}=m$

$\rm\longrightarrow\:-1=m$

$\rm\longrightarrow\:m=-1$

Hence,the value of m will be -1,