Question

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

Answer 1

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Answer 2

${\huge {\underbrace {\bf {Question}}}}$

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

${\huge {\underbrace {\bf {Answer}}}}$

${\sf {2x + 3y = 11}}$ ------- ( i )

${\sf {2x - 4y = -24}}$ ------- ( ii )

From eq. ( i ) we get,

${\sf {x = \frac {11 - 3y}{2}}}$ ----- ( iii )

To find the value of 'y'

Substitute the value of 'x' in eq ( ii )

$\implies {\sf {2x - 4y = -24}}$

$\implies {\sf { \not {2} \frac {11 - 3y}{ \not {2}} - 4y = -24}}$

$\implies {\sf {11 - 3y - 4y = -24}}$

$\implies {\sf {11 - 7y = -24}}$

$\implies {\sf {-7y = -24 - 11}}$

$\implies {\sf {-7y = - 35}}$

$\implies {\sf {y = \frac { - 35}{-7}}}$

$\implies {\green {\underline {\boxed {\sf {y = 5}}}}}$

To find value of 'x'

Substitute the value of 'y' in eq. ( iii )

$\implies {\sf {x = \frac {11 - 3y}{2}}}$

$\implies {\sf {x = \frac {11 - 3 × 5}{2}}}$

$\implies {\sf {x = \frac {11 - 15}{2}}}$

$\implies {\sf {x = \frac {-4}{2}}}$

$\implies {\green {\underline {\boxed {\sf {x = -2}}}}}$

To find the value of 'm'

Substitute the value of 'x' and 'y' into the equation y = mx + 3

$\implies {\sf {5 = m (-2) + 3}}$

$\implies {\sf {5 = -2m + 3}}$

$\implies {\sf {5 - 3 = -2m}}$

$\implies {\sf { \not {2} = - \not {2m}}}$

$\implies {\green {\underline {\boxed {\sf {m = -1}}}}}$