Question

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

Answer 1

${\huge{\red{\sf{Given}}}}\begin{cases}\leadsto 2x+3y=11 \\\leadsto 2x-4y =-24 \end{cases}$

${\huge{\red{\sf{To\:Find}}}}\begin{cases}\leadsto To\:find\:value\:of\:y\\\leadsto To\:find\:m\end{cases}$

$\huge\red{\underline{\bf{\green{Answer}}}}$

We have,

• 2x+3y=11. .............. (1)
• 2x-4y=-24. ...............(2)

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So, on subtracting (2) from (1) , we have,

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

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

$\implies \cancel{2x}+3y-\cancel{2x}+4y=35$

$\implies 7y =35$

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

$\implies y =\dfrac{\cancel{35}^{5}}{\cancel{7}}$

${\underline{\boxed{\red{\mapsto y=5}}}}$

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Now, $\red{\sf{y=mr+3}}$

$\sf{\purple{\leadsto Putting\: y =5}}$

$\implies 5 = mr + 3$

$\implies mr =(5-3)$

$\implies mr =2$

${\underline{\boxed{\red{\sf{\therefore m =\dfrac{2}{r}}}}}}$

$\large\red{\underline{\purple{\mapsto So\:\:m =\dfrac{2}{r}}}}$

Answer 2

$\huge \boxed{ \bf \red{answer}}$

2x + 3y = 11 .......(i)

2x - 4y = -24......(ii)

solving these equations by substitution method,

Now, from (ii), we get,

2x-4y=-24

2x=-24+4y

x=(-24+4y)/2

x=-24/2+4y/2

x=-12+2y...........(iii)

Put this value of x in (i), we get,

2(-12+2y) + 3y = 11

-24+4y+3y=11

7y=11+24

7y=35

y=35/7

y=5

now put this value of y in (iii)

=-12+2y

=-12+2(5)

=-12+10

=-2

y=mx+3 {y=5,x=-2)

5=m(-2)+3

5=-2m+3

5-3=-2m

2=-2m

2/2=-m

1=-m

-1=m