Question

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

Answer 1

Step-by-step explanation:

Given equations are

2x+3y=11−−−−(1)

2x−4y=−24−−−−(2)

Form (1)

2x+3y=11

⇒2x=11−3y

⇒x= 11−3y/2 −−−(3)

substituting x in(2)

2x−4y=−24

⇒2( 11−3y/2)−4y = −24

⇒11−3y−4y=−24

⇒11−7y=−24

⇒7y=35

⇒y=35/7

⇒y=5.

putting y = 5 in (3)

x= 11−3(5)/2

⇒x= 11−15/2

⇒x=−4/2

∴x=−2.

Hence x = -2 and y = 5 is the solution of the

equation.

Now, we have to find m

y=mx+3

∴m=−1

5=3(−2)+3

5−3=−2m⇒−2m=2

⇒m=−2 ; x=−1

hope it is helpful mark as brainlist..

Answer 2

Let 2x + 3y = 11 be equation (I) and, 2x - 4y = -24 be equation (ii).

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Therefore,⠀⠀⠀⠀⠀

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$\underline{\bf{\dag} \:\mathfrak{From\; equation\;(I)\: :}}$⠀⠀⠀⠀

$:\implies\sf 2x + 3y = 11 \\\\\\:\implies\sf 2x = 11 - 3y\\\\\\:\implies\sf x = \dfrac{11 - 3y}{2}$

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$\underline{\bf{\dag} \:\mathfrak{Putting\: x \; equation\;(2)\: :}}$⠀⠀

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$:\implies\sf 2x - 4y = -24\\\\\\:\implies\sf \cancel{\;2}\;\bigg( \dfrac{11 - 3y}{\cancel{\:2}}\bigg) - 4y = -24\\\\\\:\implies\sf 11 - 3y - 4y = -24\\\\\\:\implies\sf 11 - 7y = -24 \\\\\\:\implies\sf -7y = -24 - 11\\\\\\:\implies\sf -7y = -35\\\\\\:\implies\sf y = \cancel\dfrac{-35}{-7}\\\\\\:\implies{\underline{\boxed{\sf{y = 5}}}}$

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$\underline{\bf{\dag} \:\mathfrak{Putting\: y \; equation\;(I)\: :}}$⠀⠀⠀

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$:\implies\sf 2x + 3y = 11\\\\\\:\implies\sf 2x + 3(5) = 11\\\\\\:\implies\sf 2x + 15 = 11\\\\\\:\implies\sf 2x = 11 - 15\\\\\\:\implies\sf 2x = -4\\\\\\:\implies\sf x = \cancel\dfrac{-4}{2}\\\\\\:\implies{\underline{\boxed{\sf{x = -2}}}}$

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$\therefore{\underline{\sf{Hence,\:value\: of \: x \; and \: y \; are \; \bf{ -2\: and\; 5}.}}}$

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Now,

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★ Finding value of 'm'

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$:\implies\sf y = mx + 3\\\\\\:\implies\sf 5 = m(-2) + 3\\\\\\:\implies\sf 5 = -2m + 3 \\\\\\:\implies\sf 5 - 3 = -2m\\\\\\:\implies\sf 2 = -2m\\\\\\:\implies\sf m = \cancel\dfrac{-2}{2}\\\\\\:\implies{\underline{\boxed{\sf{\pink{m = -1}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \;value\:of\:'m'\:is\; \bf{-1 }.}}}$