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Question
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
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`
⇒ x = `(-4)/2`
⇒ x = -2
Hence, x = -2, y = 5
Also
y = mx + 3
5 = -2m + 3
-2m = 2
m = -1
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