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Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

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#### Solution

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

2x – 4y = – 24 ...(2)

From equation (1), we obtain

2x + 3y = 11

⇒ 2x = 11 - 3y

⇒ `x = (11-3y)/2` ...(3)

Substituting this value in equation (2), we obtain

`2((11 - 3y)/2) - 4y = -24`

⇒** **11 - 3y-4y = -24

⇒ -7y = - 35

⇒ `y = 35/7`

⇒ y = 5 ...(4)

Putting this value in equation (3), we obtain

`x = (11-3xx5)/2`

⇒ `x =( 11 - 15)/2`

⇒`(-4)/2`

⇒ -2

Hence, x = -2, y = 5

Also

y = mx + 3

5 = -2m + 3

-2m=2

m = -1

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