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Find a,b if (1,3) is solution of the system ax+2y=5 and x-by=3?

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greynose | Student, Undergraduate | Honors

Posted August 4, 2011 at 8:03 PM via web

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Find a,b if (1,3) is solution of the system ax+2y=5 and x-by=3?

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giorgiana1976 | College Teacher | Valedictorian

Posted August 4, 2011 at 8:10 PM (Answer #1)

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Since the pair of coordinates (1,3) represents the solution of the given system, that means that  plugging the values 1 and 3 in the equations, they will remain true.

a*1 + 2*3 = 5

a + 6 = 5

a = 5 - 6

a = -1

1 - b*3 = 3

1 - 3b = 3

-3b = 3 - 1

-3b = 2

b = -2/3

The requested values of a and b, if the pair (1,3) represents the solution of the system, are: a = -1 and b = -2/3.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 4, 2011 at 8:10 PM (Answer #2)

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We have to find a and b if (1, 3) is a solution set of ax+2y=5 and x-by=3

As (1, 3) is a solution we have

a + 2*3 = 5

=> a =-1

1 - 3b = 3

=> b = -2/3

The value of a = -1 and b =-2/3

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