If 0.4x + 0.16y = 1.7 and 0.3x + 0.12y = 3.4, then which of the following is correct?

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Accepted Answer

Given the system:
0.4x + 0.16y = 1.7  ...(1)
0.3x + 0.12y = 3.4  ...(2)

Step 1: Check the ratios of coefficients:
Coefficient of x: 0.4 and 0.3
Coefficient of y: 0.16 and 0.12
Constants: 1.7 and 3.4

Calculate ratios:
(0.4 / 0.3) = 4/3 ≈ 1.3333
(0.16 / 0.12) = 4/3 ≈ 1.3333
(1.7 / 3.4) = 1/2 = 0.5

Step 2: Analyze ratios:
Since (coefficient of x ratio) = (coefficient of y ratio) but not equal to (constant ratio), the system is inconsistent.

Step 3: Conclusion:
The system has no solution because the lines represented by the equations are parallel but distinct.

Hence, the correct option is: The system has no solution.

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