Question

$I.2x+3y=14$
$II.4x+2y=16$

• A. $x\ge y$
• B. $x>y$
• C. $x\le y$
• D. $x<y$
• E. $x=y$ or no relation can be established between x and y

Answer 1

The correct option is D $x<y$

2x + 3y = 14 ...(i)
4x + 2y = 16 ...(ii)
On multiply Eq. (i) by 2 then substract Eq. (ii) from this,
$\because 4x+6y-(4x+2y)=28-16$
$\Rightarrow 6y-2y=12$
$\Rightarrow 4y=12$
$\therefore y=\frac{12}{4}=3$
From Eq.(i).
$\Rightarrow 2x+3\left(3\right)=14$
$\Rightarrow 2x+9=14$
$\Rightarrow 2x=5$
$\therefore x=\frac{5}{2}$
Hence, y > x
Alternate Method
Equation I
2x + 3y = 14
2x = 14 - 3y
$x=\frac{14-3y}{2}$
On putting the value of x in Eq (i).
2x + 3y = 14
2x + 3(3) = 14
$2x=14-9\Rightarrow x=\frac{5}{2}$
Hence, y > x