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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$\huge\color{cyan}\boxed{\colorbox{black}{Question ❤}}$

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

$\huge\color{cyan}\boxed{\colorbox{black}{Answer❤}}$

$\huge\color{red}\boxed{\colorbox{black}{-1}}$

$\huge\color{cyan}\boxed{\colorbox{black}{To find}}$

Value of m

$\huge\color{cyan}\boxed{\colorbox{black}{Solution❤}}$

$2x + 3y = 11 \: (eq.\: 1)$

$2x \: – \: 4y = -24(eq. \: 2)$

$subtracting \: eq \: 1from \: 2$

$2x \: - \: 4y - (2x + 3y) = -24 - 11$

$= > 2x - 4y - 2x - 3y \\ = - 35 \\ \\ = > \: 7y \: = - 35 \\ \\ y \: = \frac{35}{7} \\ \\ = > y \: = 5$

$now, \\ \\for \: the \: value \: of \: x, \\ in \: equation \: 1 \\ putting, \: the \: value \\ of \: y \: \\ 2x + 3y = 11$

$= > 2x \: + 3 \times 5 = 11 \\ \\ (value \: of \: y \: = 5) \\ \\ = > 2x \: + \: 15 \: = 11 \\ \\ = > \: 2x \: = 11 - 15 \\ \\ 2x = - 4 \\ \\ = > x = \frac{4}{2} \\ \\ = > x \:= 2$

$now \: we \: have \: the \: value \\ of \: x \: and \: y \\ \\ so \: putting \: it \: in \\ y = mx + 3$

$= > 5 = m \times - 2 +4 \\ \\ = > 5-3 = m \times -2 \\ \\=> 2 \: = -2m\\ => \frac{2}{-2} = m \\ \\=> -1 = m$

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Answer 2

$\\ \tt \: 2x + 3y = 11 \qquad \quad \: (1) \\ \\ \tt \: 2x - 4y = - 24 \qquad \quad\: (2) \\ \\ \small{ \tt \: From \: equation \: (1), \: we \: get } \\ \\ \tt \: x = \frac{11 - 3y}{2} \qquad \quad \: (3) \\ \\ \small{ \tt \: Substituting \: this \: value \: in \: equation \: (2), \: we \: get} \\ \\ \rm \: 2 \: \bigg( \frac{11 - 3y}{2} \bigg) \: - 4y = - 24 \\ \\ \\ \rm \: 11 - 3y - 4y = - 24 \\ \\ \\ \rm \: - 7y = - 35 \\ \\ \\ \rm \: \frac{ - 35}{ - 7} \\ \\ \\ \implies \tt{ \blue{y = 5}} \qquad \quad \:( 3) \\ \\ \small{ \tt \: Putting \: this \: value \: in \: equation \: (3), \: we \: get } \\ \\ \\ \tt \: x = \frac{11 - 3 \times 5}{2} = \frac{4}{2} = - 2 \\ \\ \bf{ \orange{Hence, \: x = - 2 \: \: and \: \: y = 5}} \\ \\ \\ \tt \: y = mx + 3 \\ \\ \tt \: 5 = m \times - 2 + 3 \\\\ \gg \huge\boxed{ \red { \frak {m = - 1}}}$