Question

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) =

Answer 1

One solution. It is (2, 1)

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.