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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 0.3x − 0.4y = 0.2 −0.2x + 0.5y = 0.1 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =

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Answer:

One solution.  It is (2, 1)

Step-by-step explanation:

Clear out all fractions right away by multiplying all terms by 10.  Then:

0.3x − 0.4y = 0.2

−0.2x + 0.5y = 0.1

becomes

3x - 4y = 2

-(2x + 5y = 1)

Multiply the first row by 2 and the second row by 3, which produces:

  6x - 8y = 4

 -6x +15y =  3

Combining like terms results in:         7y = 7.  Then y = 1.

Now subst. 1 for y in the first equation, to calculate x:

3x - 4(1) = 2

3x          = 2 + 4  = 6.  Then x = 2.

The solution is (2, 1).  There is ONLY ONE SOLUTION.

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