Question

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

Answer 1

The value of m is $\mathbf{-\frac{31}{55}}$

Step-by-step explanation:

• Given data

         2 x -4 y = -24 y            ...1)

         2 x = -24 y + 4 y

         2 x = - 20 y

         x = - 10 y                      ... 2)

• Now come to second equation

        2 x + 3 y = 11          (Put value x in term of y)

        2 (-10 y) + 3 y = 11

        -20 y + 3 y = 11

        -17 y = 11

         So

         $\mathbf{y =-\frac{11}{17}}$                       ...3)

• Then

        $\mathbf{x =-10\times \left ( -\frac{11}{17} \right )=\frac{110}{17}}$        ...4)

• Now come to equation

        y = m x + 3       ( put value of x and y)

        $\mathbf{-\frac{11}{17}=m\left ( \frac{110}{17} \right )+3}$

        $\mathbf{m\left ( \frac{110}{17} \right )=-3-\frac{11}{17}}$

        $\mathbf{m\left ( \frac{110}{17} \right )=-\frac{62}{17}}$

        $\mathbf{m=-\frac{62}{17}\times \frac{17}{110}=-\frac{62}{110}=-\frac{31}{55}}$

Answer 2

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2x + 3y = 11…………………………..(i)

2x + 3y = 11…………………………..(i)2x – 4y = -24………………………… (ii)

From equation (ii), we get;

x = (11 – 3y)/2 ……….…………………………..(iii)

Putting the value of x in equation (ii), we get

2[(11 – 3y)/2] – 4y = −24

11 – 3y – 4y = -24

-7y = -35

y = 5……………………………………..(iv)

Putting the value of y in equation (iii), we get;

x = (11 – 15)/2 = -4/2 = −2

Hence, x = -2, y = 5

Also,

y = mx + 3

5 = -2m +3

-2m = 2

m = -1

Therefore, the value of m is -1

Hope it's Helpful....:)