Question

(8) 49x - 57y = 172; 57x - 49y = 252​

Answer 1

Step-by-step explanation:

Logarithm of 125 to base 55 is

log55125=log5553=log52353=3.32=2

Logarithm of .25 to base 4 is 

log40.25=log220.52=21.log20.52=21.log22−2=21(−2)=−1

Answer 2

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49x – 57y = 172 ....(I)

57x – 49y = 252 ...(II)

Adding (I) and (II)

49x+57x-57y-49y=172+252

⇒106x-106y=424

⇒x-y=4 ...(III)

Subtracting (II) from (I) we have

49x-57y-57y-(-49y)=252-172

⇒-8x-8y=-80

⇒-x-y=-10

⇒x+y=10 ..(IV)

Adding (III) and (IV)

x-y=4x+y=10⇒2x=14⇒x=7

Putting the value of x = 7 in (IV) we get

7+y=10⇒y=10-7⇒y=3

Thus, (x, y) = (7, 3).