Multiple choice

Solve the equation: $5x -2 y = 6$ and $2x + 5y = 3$ and then identify the system of equation.

  1. Consistent

  2. Inconsistent

  3. Dependent

  4. All the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a system a1x + b1y = c1 and a2x + b2y = c2, if a1/a2 != b1/b2, the system is consistent and independent. Here, 5/2 != -2/5, so it is consistent.

AI explanation

To check for consistency, compare the ratio of the coefficients of x, y, and the constants for both equations. For the given equations 5x - 2y = 6 and 2x + 5y = 3, the ratios are 5/2, -2/5, and 6/3. Since these ratios are not equal, the lines intersect at exactly one unique point. Therefore, the system is consistent.

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