Solve 2x + 3y =11 and 2x - 4y = -24 and hence, the value of m for which y = mx + 3 is ____

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Detailed Solution

Solve 2x + 3y =11 and 2x - 4y = -24 and hence, the value of m for which y = mx + 3 is -1.
Given two equations 2x + 3y =11 and 2x - 4y = -24.
According to the question,
2x + 3y = 11
3y = 11 - 2x

y = 11 − 2 x 3

Also, other equation is,
2x - 4y = -24
Putting the value of y using substitution method,

2 x − 4 11 − 2 x 3 = − 24

2 x − 44 + 8 x 3 = − 24

6 x − 44 + 8 x 3 = − 24

6 x + 8 x = − 72 + 44

14 x = − 28

x = -2
Now, the value of y is,

2 (− 2) + 3 y = 11

3 y = 15

y = 5
Now, the value of m by putting value of x and y in equation,
y = mx + 3
5 = m(-2) + 3
-2m = 5 - 3
-2m = 2
m = -1
Therefore, m = -1.

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