10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Case Based (MCQs) - Pair of Linear Equations in Two Variables

Write the number of solutions of the system of linear equations \[\text{2x}-\text{3y}+\text{4}=0\] and \[\text{x}+\text{2y}-\text{5=0}\].

A) 1

B) 2

C) 0

D) infinite

Correct Answer: A

Solution :

For the given system of equations, we have

\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{1}=2;\,\,\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-3}{2}=-\frac{3}{2}\]

i.e., \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \,\,\,\frac{{{b}_{1}}}{{{b}_{2}}}\]

So, the given system of equations are intersecting in nature.

So, they will have only one solution.

So, option [a] is correct.