Question

If 3x +2y - 5 = 0, 2x – 3y + 4 = 0
then (x, y) =​

Answer 1

(x,y) = (7/13 , 22/13)

Step-by-step explanation:

Given :-

3x +2y - 5 = 0,

2x – 3y + 4 = 0

To find :-

Find (x, y) ?

Solution :-

Given equations are :-

3x +2y - 5 = 0

=> 3x + 2y = 5 --------(1)

On multiplying with 3 both sides

=> 9x+6y = 15 ---------(2)

2x – 3y + 4 = 0

=> 2x - 3y = -4 --------(3)

On multiplying with 2 both sides

=> 4x-6y = -8 ---------(4)

On adding (2)&(4) then

9x + 6y = 15

4x - 6y = -8

(+)

__________

13x + 0 = 7

__________

=> 13x = 7

=> x = 7/13

On Substituting the value of x in (1) then

3x + 2y = 5

=> 3(7/13)+2y = 5

=> (21/13)+2y = 5

=> 2y = 5-(21/13)

=> 2y = (65-21)/13

=> 2y = 44/13

=> y = 44/(13×2)

=> y = 44/26

=> y = 22/13

Therefore, x = 7/13 and y = 22/13

Answer:-

The value of (x,y) = (7/13 , 22/13) for the given problem.

Check:-

if x = 7/13 and y = 22/13 then

3x +2y - 5

=> 3(7/13)+2(22/13)-5

=> (21/13)+(44/13)-5

=> (21+44-65)/13

=> (65-65)/13

=> 0/13

=> 0

3x +2y - 5 = 0 verified.

2x – 3y + 4

=> 2(7/13)-3(22/13)+4

=> (14/13)-(66/13)+4

=> (14-66+52)/13

=> (66-66)/13

=> 0/13

=> 0

2x – 3y + 4 = 0 Verified.

Used Method:-

• Elimination method