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

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Unformatted text preview: Solutions to Quiz 12A www.math.ufl.edu/˜harringt October 31, 2007 1. Find the solution set for each system. 1 x 2 1 x 4 + 1y = 3 3 − 2 y = −1 3 1 x 2 1 x 4 (a) + 1y = 3 3 ⇒ − 2 y = −1 3 1 6( 1 x + 3 y ) = 6(3) 2 ⇒ 2 −12( 1 x − 3 y ) = −12(−1) 4 3x + 2y = 18 −3x + 8y = 12 Next, if we use elimination, we have the following: 3x + 2y −3x + 8y −−−−− 10y = = − = 18 12 −− 30 Thus, y = 3. To solve for x, we can plug y = 3 into 3x + 2y = 18. So we have: 3x + 2(3) = 18 3x = 12 x=4 So the solution set is {(4, 3)}. (b) 3 x 2 − 1y = 7 2 2 9x − 3y = 21 − 1y = 7 2 2 ⇒ 9x − 3y = 21 3 x 2 3 7 2( 2 x − 1 y ) = 2( 2 ) 2 ⇒ 9x − 3y = 21 1 3x − y = 7 9x − 3y = 21 So our system can be reduced to: 9x − 3y = 21 9x − 3y = 21 By using elimination, we have that 0 = 0 so that the system is dependant. So we have infinitely many solutions! (We can not write each individual solution so we must use set notation.) Our solution set is {(x, y ) : 9x − 3y = 21}. 2. If a system of equations has no solution it is said to be inconsistant. 2 ...
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quiz 12A sol - Solutions to Quiz 12A...

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