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

Find the points where the lines represented by the equations \[\text{2x}-\text{5y}+\text{4}=0\]and \[\text{x}+\text{2y}-\text{5}=0\]respectively intersect the x-axis.

A) \[(-3,0)\] and \[(4,0)\]

B) \[(-2,0)\] and \[(5,0)\]

C) \[(-1,0)\] and \[(6,0)\]

D) \[(2,0)\] and \[(4,0)\]

Correct Answer: B

Solution :

On x-axis \[y=0\].

So. substituting \[y=0\] in the equations \[2x-3y+4=0\] and \[x+2y-5=0,\] we get

\[2x-3(0)+4=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2x+4=0\,\Rightarrow x=-2\]

and \[x+2(0)-5=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x-5=0\Rightarrow \,\,x=5\]

Hence, the given system of equations will intersect x-axis at points \[(-2,0)\] and \[(5,0),\] respectively.

So. option [b] is correct.