Question

The pair of linear equations \( \frac{3}{2}x + \frac{5}{3}y = 7 \) and \( 9x - 10y = 14 \) is:

• A. \text{Consistent}
• B. \text{Inconsistent}
• C. \text{Dependent}
• D. \text{None of these}

Hint:

Inconsistent systems have parallel lines with no solution.

Answer 1

The Correct Option is B

For two equations \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \):
- If \( \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \), they are inconsistent (parallel lines, no solution).
- Here, checking coefficients:
\[ \frac{\frac{3}{2}}{9} = \frac{1}{6}, \quad \frac{\frac{5}{3}}{-10} = -\frac{1}{6}. \] Since these ratios are not equal, the equations are inconsistent.