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

The value of x and y for the following system of equations \[x+8y=19\]and\[2x+11y=28\], (by substitution method) is

A) 3,2

B) 2,3

C) 6,3

D) 3,4

Correct Answer: A

Solution :

Given equations are

\[x+8y=19\] ...(i)

and \[2x+11y=28\] ...(ii)

From Eq.(i), \[x=19-8y\] ...(iii)

On substituting \[x=19-8y\]in Eq. (ii), we get

\[2\left( 19-8y \right)+11y=28\]

\[\Rightarrow \,\,38-16y+11y=28\]

\[\Rightarrow \,\,\,5y=38-28=10\]

\[\Rightarrow \,\,\,\,y=\frac{10}{5}=2\]

Now, on putting y = 2 in Eq. (iii), we get

\[x=19-8\times 2\]

\[\Rightarrow \,\,\,x=19-16=3\]

Thus, \[x=3\]and y = 2 is the required solution.