Question

Solve the following systems by Elmination by Substitution method.
x/3+y/4=4 ; 5x/6-y/8=4
The answer is x = 6 , y= 8

Answer 1

Hiii friend,

X/3 + Y/4 => 4.

4X + 3Y/12 = 4

4X + 3Y = 12 × 4

4X + 3Y = 48......(1)

5X/6 - Y/8 = 4

5X × 4 - Y × 3 /24 = 4

20X - 3Y/24 = 4

20X - 3Y = 24×4

20X - 3Y = 96....(2)

USING SUBSTITUTION METHOD.


From equation (1) we get,



4X + 3Y = 48

4X = 48-3Y

X = 48-3Y/4.....(3)

Putting the value of X in equation (2)

20X - 3Y = 96

20 × (48-3Y/4) - 3Y = 96

5(48-3Y) - 3Y = 96

240 - 15Y -3Y = 96

-18Y = 96-240

-18Y = -144

Y = -144/-18 => 8

Putting the value of Y in equation (3)

X = 48-3Y/4 => 48 - 3 × 8 /4 => 48-24/4

X = 24/4 => 6.

Hence,

X = 6 and Y = 8


Again, By elmination method.


X/3 + Y/4 = 4

4X + 3Y = 48......(1)

And,

5X/6 - Y/8 = 4


20X - 3Y = 96.....(2)


Subtract equation (1) by equation (2)

20X - 3Y = 96
4X +3Y = 48
_____________

24X = 144

X = 144/24 => 6

Putting the value of the in equation (1)

4X + 3Y = 48

4 × 6 + 3Y = 48

24 + 3Y = 48

3Y = 48-24

3Y = 24

Y = 24/3 => 8


Hence,

X = 6 and Y = 8.



HOPE IT WILL HELP YOU.... :-)

Answer 2

Elimination method.

X/3 + Y/4 = 4

4X + 3Y = 48......(1)

5X/6 - Y/8 = 4

20X - 3Y = 96.....(2)

Subtract equation (1) by equation (2)

20X - 3Y = 96

4X +3Y = 48

_____________

24X = 144

X = 144/24 => 6

In eq. 1

4X + 3Y = 48

4 × 6 + 3Y = 48

24 + 3Y = 48

3Y = 48-24

3Y = 24

Y = 24/3 => 8

X = 6 and Y = 8.