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

Q2.    Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.

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Given, two equations,

2x + 3y = 11......(1)

2x - 4y = -24.......(2)

Now, from (1), we have 

y=\frac{11-2x}{3}........(3)

Substituting this in (2), we get 

2x-4\left ( \frac{11-2x}{3} \right )=-24

\Rightarrow 6x-44+8x=-72

\Rightarrow 14x=44-72

\Rightarrow 14x=-28

\Rightarrow x=-2

Substituting this value of x in (3)

\Rightarrow y=\left ( \frac{11-2x}{3} \right )=\frac{11-2\times(-2)}{3}=\frac{15}{3}=5

Hence, Solution of the given equations is,

x=-2,\:and\:y=5.

Now,

As it satisfies  y=mx+3,

\Rightarrow 5=m(-2)+3

\Rightarrow 2m=3-5

\Rightarrow 2m=-2

\Rightarrow m=-1

Hence Value of m is -1.

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