10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

Using elimination method, all the possible solutions of the following pair of linear equations is \[2x+3y=8\]and \[4x+6y=7\]

A) Consistent

B) \[x=2,y=3\]

C) No solution

D) All real values

Correct Answer: C

Solution :

Given, pair of linear equations is

\[2x+3y=8\] ... (i)

and \[4x+6y=7\] (ii)

On multiplying Eq. (i) by 2, to make the coefficients of x equal, we get the equation as

\[4x+6y=16\] ... (iii)

On subtracting Eq. (ii) from Eq. (iii), we get

\[\left( 4x-4x \right)+(6y-6y)=16-7\]

\[\Rightarrow \,\,\,0=9\]

which is a false equation involving no variable.

So, the given pair of linear equations has no solution, i.e. this pair of linear equations is inconsistent