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quiz 12A sol - Solutions to Quiz 12A...

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Solutions to Quiz 12A www.math.ufl.edu/˜harringt October 31, 2007 1. Find the solution set for each system. (a) 1 2 x + 1 3 y = 3 1 4 x - 2 3 y = - 1 1 2 x + 1 3 y = 3 1 4 x - 2 3 y = - 1 6( 1 2 x + 1 3 y ) = 6(3) - 12( 1 4 x - 2 3 y ) = - 12( - 1) 3 x + 2 y = 18 - 3 x + 8 y = 12 Next, if we use elimination, we have the following: 3 x + 2 y = 18 - 3 x + 8 y = 12 - - - - - - - - 10 y = 30 Thus, y = 3. To solve for x , we can plug y = 3 into 3 x + 2 y = 18. So we have: 3 x + 2(3) = 18 3 x = 12 x = 4 So the solution set is { (4 , 3) } . (b) 3 2 x - 1 2 y = 7 2 9 x - 3 y = 21 3 2 x - 1 2 y = 7 2 9 x - 3 y = 21 2( 3 2 x - 1 2 y ) = 2( 7 2 ) 9 x - 3 y = 21 3 x - y = 7 9 x - 3 y = 21 1
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So our system can be reduced to:
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