Question

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

Answer 1

Solution:-

Given

$\rm \implies \: 2x + 3y = 11 \: \: \: \: \: \: \: .....(i)eq$

$\rm \implies \: 2x - 4y = - 24 \: \: \: \: \: \: .... (ii)eq$

Using Elimination method

Subtract ( ii ) eq from ( i )eq

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

$\rm \implies \: 7y = 35$

$\rm \implies \: y = \dfrac{35}{7} = 5$

$\rm \implies \: y = 5$

Put the value of y on (i) eq

$\rm \implies \: 2x + 3y = 11 \: \: \: \: \: \: \: .....(i)eq$

$\rm \implies \: 2x + 3 \times 5 = 11$

$\rm \implies \: 2x + 15 = 11$

$\rm \implies \: 2x = 11 - 15$

$\rm \implies2x = - 4$

$\rm \implies \: x = - 2$

Now put the value of x and y on

$\rm \implies \: y = mx \: + 3$

Where

$\rm \implies \: x \: = - 2 \: \: and \: \: y = 5$

put the value

$\rm \implies \: 5 = m \times - 2 + 3$

$\rm \implies \: 5 = - 2m \: + 3$

$\rm \implies \: 5 - 3 = - 2m$

$\rm \implies \: 2 = - 2m$

$\rm \implies \: m = - 1$

So value of m = - 1