Question

43x+57y=257 and 57x+43y=243 so x-y= ?​

Answer 1

43x+57y=257...(I)

57x+43y=243...(II)

Adding (I) and (II)

43x+57x+57y+43y=257+243

⇒100x+100y=500

⇒100(x+y)=500

⇒x+y=500/100

⇒x+y=5...(III)

Subtracting (II) from (I) we have

43x+57y−(57x+43y)=257−243

⇒43x+57y-57x-43y=14

⇒-14x+14y=13

⇒-14(x-y)=13

⇒x-y= -13/14...(IV)

Adding (III) and (IV)

x+y=5

x-y=-13/14

⇒2x=4.072

⇒x=2

Putting the value of x = 2 in (III) we get

2+y=5

⇒y=5-2

⇒y=3

Thus, (x,y)=(2,3)

Answer 2

Answer:

43x+57y=257...(I)

57x+43y=243...(II)

Adding (I) and (II)

43x+57x+57y+43y=257+243

⇒100x+100y=500

⇒100(x+y)=500

⇒x+y=500/100

⇒x+y=5...(III)

Subtracting (II) from (I) we have

43x+57y−(57x+43y)=257−243

⇒43x+57y-57x-43y=14

⇒-14x+14y=13

⇒-14(x-y)=13

⇒x-y= -13/14...(IV)

Adding (III) and (IV)

x+y=5

x-y=-13/14

⇒2x=4.072

⇒x=2

Putting the value of x = 2 in (III) we get

2+y=5

⇒y=5-2

⇒y=3

Thus, (x,y)=(2,3)

Step-by-step explanation: