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Solve $2x + 3y = 11$ and $2x β 4y = β 24$ and hence find the value of β$m$β 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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