What conclusion can be drawn about the solution of the following system of linear equations in two variables: 3x + 2y = 7 and 2x + 3y = 7?

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Accepted Answer

To determine the nature of the solution of the system:

Given equations:
1) 3x + 2y = 7
2) 2x + 3y = 7

Step 1: Calculate the determinant (D) of the coefficient matrix:
D = (3)(3) - (2)(2) = 9 - 4 = 5

Since D ≠ 0, the system has a unique solution.

Step 2: For completeness, find the solution:
Dx = |7 2|
     |7 3| = (7)(3) - (7)(2) = 21 - 14 = 7

Dy = |3 7|
     |2 7| = (3)(7) - (2)(7) = 21 - 14 = 7

x = Dx / D = 7 / 5 = 1.4

y = Dy / D = 7 / 5 = 1.4

Therefore, the system has a unique solution (x, y) = (1.4, 1.4).

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