Question

In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:

I. 8x + y = 10
II. 4x + 2y = 13

• A. if x > y
• B. if x < y
• C. if x ≥ y
• D. if x ≤ y
• E. if x = y or definite relationship cannot be established between ‘x’ and ‘y’

Answer 1

The correct option is B if x < y

$I.8x+y=10$
$II.4x+2y=13$
On solving eqn (i) and (ii), we get
$16x+2y=20\cdots \left(iii\right)$
$4x+2y=13\cdots \left(iv\right)$
$---$
$\underset{–}{}$ (Changing the signs of the second equation)
$12x=7x=\frac{7}{12}$
Putting the value of x in eqn (i) we get
$8\times \frac{7}{12}+y=10y=10-\frac{14}{3}=\frac{16}{3}$
Hence, $x<y.$