Question

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

Answer 1

Answer:

hope it will help you:-)

Answer 2

AnswEr:

$\dag$ 2x + 3y = 11 --------Eq(1)

$\dag$ 2x - 4y = -24 ---------Eq(2)

From Equation (1)

$\sf\; x \; = \; \dfrac{11 \; - \; 3y}{2}$ -------Eq(3)

$\small\bold{\underline{\sf{Now,\; Substituting\; the\; Value\; of \; x\; in\; Eq(2)}}}$

$\longrightarrow\sf\; 2(\dfrac{11 - 3y}{2}) - 4y = -24$

$\longrightarrow\sf\; 11 - 3y - 4y =-24$

$\longrightarrow\sf\; -7y = -35$

$\longrightarrow\sf\; \dfrac{-35}{-7}$

$\longrightarrow\large{\underline{\boxed{\sf{\pink{y\; = \; 5}}}}}$

$\rule{150}2$

$\small\bold{\underline{\sf{Now,\; Substituting\; the\; Value\; of \; y\; in\; Eq(3)}}}$

$\longrightarrow\sf\; x = \dfrac{11 - 3(5)}{2}$

$\longrightarrow\sf\; x = \dfrac{-4}{\;\;2}$

$\longrightarrow\large{\underline{\boxed{\sf{\red{x \; = \; -2}}}}}$

$\rule{150}2$

★ Now, Finding the Value of m.

$\longrightarrow\sf\; y = mx + 3$

$\longrightarrow\sf\; 5 = -2m + 3$

$\longrightarrow\sf\; -2m = 2$

$\longrightarrow\sf\; m \; = \;\dfrac{\;\;2}{-2}$

$\longrightarrow\large{\underline{\boxed{\sf{\pink{m\; = \; -1}}}}}$

Hence, Value of m is -1.

$\rule{150}2$