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

Given:

Given pair of linear equations are

$2x + 3y = 11$ and $2x – 4y = – 24$

To do:

We have to find the value of ‘$m$’ for which $y = mx + 3$.

Solution:

Given equations are:

$2x + 3y = 11$.....(i)

$2x – 4y = – 24$.......(ii)

From equation (i),

$2x = 11 – 3y$

Putting this value in equation (ii), we get,

$11 – 3y – 4y = -24$

$11 – 7y = -24$

$7y = 11+24$

$7y=35$

$y = \frac{35}{7}$

$y = 5$

Putting $y = 5$ in equation (i), we get,

$2x + 3(5) = 11$

$2x + 15 = 11$

$2x = 11 - 15$

$2x = -4$

$x = -2$

Putting the value of $x$ and $y$ in equation $y = mx + 3$, we get,

$5 = -2m + 3$

$5-3 = -2m$

$2m = 2$

$m=1$

**Hence, the value of $m$ is $1$.**

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