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) =
Accepted Solution
A:
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 = 0.1becomes3x - 4y = 2-(2x + 5y = 1)Multiply the first row by 2 and the second row by 3, which produces: 6x - 8y = 4 -6x +15y = 3Combining like terms results in: 7y = 7. Then y = 1.Now subst. 1 for y in the first equation, to calculate x:3x - 4(1) = 23x = 2 + 4 = 6. Then x = 2.The solution is (2, 1). There is ONLY ONE SOLUTION.