Question

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

Answer 1

Given equations are 

2x+3y=11−−−−(1)

2x−4y=−24−−−−(2)

Form (1)

2x+3y=11 

⇒2x=11−3y

⇒x=211−3y−−−(3)

substituting  x in(2)

2x−4y=−24 

⇒2(211−3y)−4y=−24

⇒11−3y−4y=−24

⇒11−7y=−24

⇒7y=35

⇒y=35/7

⇒y=5.

putting  y = 5 in (3) 

x=211−3(5)

⇒x=211−15

⇒x=196

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Answer 2

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