Question

By substitution method solve : x+1/2 + y-1/3 = 8 , x-1/3 + y+1/2 = 9. (class 10th )​

Answer 1

$\large{\underline{\red{\rm{AnswEr:X=7,\:\:\:Y=13}}}}$

$\huge\bold\green{\underline{Solution:}}$

$\bold\red{\underline{Given\:equation:}}$

X+1/2+Y-1/3=8

X-1/3+Y+1/2=9

At first we have to simplify this equation

⟹X+1/2+Y-1/3=8

⟹3X+3+2Y-2/6=8

⟹3X+2Y=48-1

⟹3X+2Y=47---------1

$\bold\purple{\boxed{3X+2Y=47----(1)}}$

⟹X-1/3+Y-1/2=9

⟹2X-2+3Y-3/6=9

⟹2X+3Y=54-1

⟹2X+3Y=53----------2

$\bold\purple{\boxed{2X+3Y=53----(2)}}$

$\bold\orange{\underline{Now,\:solving\: equation\:by\: substituting\: method}}$

Solve the 1 equation to find the valve of X than substituting in equation 2

⟹3X+2Y=47

⟹3X=47-2Y

⟹X=47-2Y/3

Now, putting the value of X in EQ 2

⟹2X+3Y=53

⟹2(47-2Y/3)+3Y=53

⟹94-4Y/3+3Y=53

⟹94-4Y+9Y/3=53

⟹94+5Y=159

⟹5Y=159-94

⟹5Y=65

⟹Y=13

Putting the value of y=13 in EQ 1

⟹3X+2Y=47

⟹3X+2×13=47

⟹3X+26=47

⟹3X=47-26

⟹3X=21

⟹X=7

Hence,

The value of X=7

The Value of Y=13