Question

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

Answer 1

$Given \: 2x + 3y = 11 \: --(1) \\and \: 2x - 4y = -24 \: --(2)$

/* subtract equation (2) from equation (1) , we get */

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

$\implies 2x + 3y - 2x + 4y= 11 + 24$

$\implies 7y= 35$

$\implies y= \frac{35}{7}$

$\implies y= 5 \: --(3)$

/* Put y = 5 in equation (1) , we get */

$2x + 3\times 5 = 11$

$\implies 2x + 15 = 11$

$\implies 2x = 11 - 15$

$\implies 2x = -4$

$\implies x = \frac{-4 }{2}$

$\implies x = -2 \: --(4)$

/* Now, put x and y values in y = mx + c , we get */

$5 = m \times (-2) + 3$

$\implies 5 - 3 = -2m$

$\implies 2 = -2 m$

$\implies \frac{2}{-2} = m$

$\therefore m = -1$

Therefore.,

$\red{ Value \: of \: m } \green { = -1}$

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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....:)