In order for a system of two linear equations to have infinitely many solutions, the two equations must be equivalent. Thus,the equation
ax+by=12 must be equivalent to the equation
2x+8y=60 Multiplying each side of
ax+by=12 by 5 gives
5ax+5by=60 which must be equivalent to
2x+8y=60 .Since the right-hand sides of
5ax+5by=60 and
2x+8y=60 are the same, equating coefficients gives
5a=2, or
a= and
5b=8 ,or
b=.Therefore,the value of
()=()÷(),which is equal to
.Either the fraction
or its equivalent decimal,25 may be gridded as the correct answer.
Alternatively, since
ax+by=12 is equivalent to
2x+8y=60,the equation
ax+by=12 is equal to
2x+8y=60 multiplied on each side by the same constant. Since multiplying
2x=8y=60 by a constant does not change the ratio of the coefficient of
x to the coefficient of y,it follows that
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