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

Solution :

We have,

2x + 3y = 11        ….(1)

and 2x – 4y = -24        ……(2)

From equation (1), we have 2x = 11 – 3y

Substituting the value of 2x = 11 – 3y in (2), we get

11 – 3y – 4y = -24

-7y = -24 – 11

-7y = -35    \(\implies\)   y = 5

Putting y = 5 in equation (1), we get

2x + 3 \(\times\) = 11

2x = 11 – 15

\(\implies\)  x = -\(4\over 2\) = -2

Hence, x = -2  and y = 5

Now put x = – 2 and y = 5 in y = mx + 3, we get

5 = m(-2) + 3      \(\implies\)   -2m = 5 – 3

\(\implies\)   m = -\(2\over 2\) = 1

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