Solve 5x + 3y = 14 and 8x + 13y = 8

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We have to solve for x and y using the equations:

5x + 3y = 14 … (1)

8x + 13y = 8 … (2)

8*(1) – 5*(2)

=> 40x + 24y – 40x – 65y = 112 – 40

=> -41y = 72

=> y = -72/ 41

5x + 3y = 14

=> 5x - 3*(72/41) = 14

=> 5x = 790/41

=> x = 158/41

**Therefore x = 158/41 and y = -72/41**

5x + 3y = 14-------(1)

8x +13y =8--------(2)

(1)*8 & (2)*5

40x + 24y =112

-40x +65y =40

_____________

-41y = 72

y= -72/41

To solve

5x + 3y = 14...(1) and 8x + 13y = 8....(2).

(1)*8-(2)*5 :

(5x+3y)8-(8x+13y)5 = 14*8-8*5 = 72.

(24-65)y = 72.

-41y = 72.

y = -72/41

(1)*13-(2)*3 :

(5x+3y)*13-(8x+13y)*3 = 14*13 -8*3 = 158.

(65-24)x = 158.

41x = 158.

x= 158/41.

Therefore x= 158/41 and y = -72/41.

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