Question

$\huge\mathfrak \red{solve \: the \: equations \: }$
✰ 4x - 18 = 3y , 6x + 7y - 4 = 0
✰ 5/x + 6y = 13 , 3/x + 4y = 7
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Answer 1

Step-by-step explanation:

Given:-

Pair of linear equations are:

1) 4x - 18 = 3y and 6x + 7y - 4 = 0

2)5/x + 6y = 13 , 3/x + 4y = 7

To find:-

Solve the given equations ?

Solution:-

1)

Given pair of linear equations are

4x - 18 = 3y

=>4x -18 -3y = 0

=>4x -3y = 18---------(1)

on multiplying with 3 then

=>12x-9y = 54 --------(2)

and 6x+7y -4 = 0

=>6x +7y = 4

on multiplying with 2 then

=>12x +14y =8--------(3)

On subtracting (3) from (2) then

12x +14y = 8

12x-9y = 54

(-)

__________

0+23y = -46

__________

=>23y = -46

=>y = -46/23

=>y = -2

In Substituting the value of y in (1) then

4x -3(-2) = 18

=>4x +6 = 18

=>4x = 18-6

=>4x = 12

=>x = 12/4

=>x = 3

The value of x = 3 and y=-2

Solution = (3,-2)

Verification:-

If x = 3 and y=-2 then

4(3)-3(-2)=13+6=18

6(3)+7(-2)=18-14=4

Verified the given relations

2)

Given equation are: 5/x + 6y = 13---------(1)

3/x + 4y = 7-------(2)

Put 1/x = a then

5a+6y = 13-------(3)

on multiplying with 3 then

15a+18y = 39------------(4)

and 3a+4y = 7-------(5)

on multiplying with 5 then

15a+20y = 35-----------(6)

On Subtracting (6) from (5) then

15a +20 y = 35

15a +18y = 39

(-)

____________

0+2y = -4

____________

=>2y = -4

=>y = -4/2

y = -2

On Substituting the value of y in (3)

=>5a+6(-2)=13

=>5a-12 = 13

=>5a = 13+12

=>5a = 25

=>a = 25/5

=>a = 5

=>a=1/x = 5

=>x = 1/5

The value of x = 1/5 and y = -2

The solution=(1/5 ,-2)

Verification:-

If x = 1/5 and y = -2 then

5/(1/5)+6(-2)

=>25-12= 13

and

3/(1/5)+4(-2)

=>15-8 = 7

Verified the given relations.

Solutions:-

Solutions are I) (3,-2) and ii)(1/5,-2)

Used method :-

Elimination method.

Answer 2

Answer:

$\huge\mathfrak \red{Answer }$

✰ 4x - 18 = 3y , 6x + 7y - 4 = 0

We will solve this by elimination method.

4x - 18 = 3y

4x - 3y - 18 = 0

So,

4x - 3y - 18 = 0 ×6

6x + 7y - 4 = 0. ×4

-----------------------------

24x - 18y - 108 = 0

24x + 28y - 16 = 0

-----------------------------

(-) (-) (+)

-----------------------------

0 - 46y - 92 = 0

-46y = 92

y = 92/-46

$\green{y = -2}$

4x - 3y - 18 = 0

4x - 3(-2) - 18 = 0

4x + 6 - 18 = 0

4x - 12 = 0

4x = 12

x = 12/4

$\green{x = 3}$