9. ( pt) Library/Utah/Intermediate.Algebra/set13.Systems.of Equations.a /s13p3.p

Question

9. ( pt) Library/Utah/Intermediate.Algebra/set13.Systems.of Equations.a /s13p3.pg A linear system may have a unique solution, no solution, or infinitely many solutions. Indicate the type of the system for the following examples by U, N orI ,respectively 2x+3y = 5 --. 2x+3y = 6 2x+3y = 5 2x+4y = 6 2x+3y = 5 Hint: If you can't tell the nature of the system by inspection, then try to solve the system and see what happens. Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America

Explanation / Answer

1)2x+3y=5, 2x+3y=6
Consider, ratio of the coefficients
2/2 = 3/3 = 5/6
Here 1 is not equal to 5/6
Hence the equations do not have no solution(N).

2)Here, the equations have Unique solution(U)

3)If you see the equations, they are both the same if you divide second equation by 2.
Hence they have infinite solutions, (I)

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