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To determine which system of equations has no solution, we look for inconsistent systems. This typically happens when two equations represent parallel lines, meaning their slopes are the same but the constants differ.

Let's check each system:
1. \( 5x + 3y = -22 \) and \( 4x - 5y = 12 \)
2. \( 2x + 3y = 45 \) and \( 2y + 4x = 30 \)
3. \( 4x - 6y = -30 \) and \( 2x - 3y = 10 \)

We need to compare the ratios of the coefficients for \( x \), \( y \), and the constants.

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Determine which system of equations has no solution.

Learn how to determine which system of equations has no solution by checking for parallel lines with the same slope but different constants. This problem involves solving systems of linear equations, focusing on identifying inconsistent systems. Ideal for Grades 8-10.

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