Question

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

Answer 1

Answer:

m = - 5 / 2

Step-by-step explanation:

Here,

2x + 3y = 11

2x = 11 - 3y

x = 11 - 3y / 2. ____________1

and

2x – 4y = - 24. _____________2

substituting 1 in 2

2(11 - 3y / 2) - 4y = -24

11 - 3y - 4y = -24

-7y = -35

7y = 35

y = 35 / 7

y = 5. _____________3

substituting 3 in 1

we get

x = 11 - 3y / 2

x = 11 - 3x5 / 2

x = - 4 / 2

x = - 2. _____________4

substituting 3 and 4 in

y = mx

5 = (m)x(-2)

m = 5 / -2

Hence

value for m is 5/2

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Answer 2

Given equations:

$2x+3y=11 \\ => 2x + 3y -11 =0 ...(i)$

$2x -4y = -24 \\ => 2x - 4y +24 = 0 ...(ii)$

To find :

The values of x and y

and,

The value of 'm' for which, $y = mx + 3$

=> $m = \frac{y-3}{x}$

Solution:

In equation (i) and (ii),

By elimination method, Eliminate 2x from both the equations, then we get,

$3y - 11 = 0$ .....(iv)

$-4y + 24 = 0$ ......(v)

By adding equation (iv) and (v), we get,

$(3y - 11) + (-4y + 24) = 0 \\ => -y + 13 = 0 \\ => -y = - 13 \\ => \bold{y = 13}$

Now, let's find the value of x,

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

$2x + 3(13) -11 = 0 \\ => 2x + 39 - 11 = 0 \\ => 2x + 28 = 0 \\ => 2x = -28 \\ => x = \frac{-28}{2} \\ =>\bold{ x = -14}$

So, we have value of x and y = -14 and 13 respectively.

Now, We have to find the value of 'm' for which $y = mx + 3$

As, we had derived a another equation from this equation to find the value of m, above, $m = \frac{y-3}{x}$.....(a)

Put values of x and y in equation (a),

$m = \frac{13-3}{-14} \\ => m = \frac{10}{-14} \\ => \bold{m = \frac{5}{-7}}$

Hence, we have value of $\bold{m =\frac{5}{-7}}$