Question

Solve the following pair of linear equations by substitution method:
$8x+5y=12$
$3x-2y=0$

• A. $x=\frac{24}{31}$ $y=\frac{36}{31}$
  
• B. $x=\frac{24}{31}$ $y=\frac{24}{31}$
  
• C. $x=\frac{36}{31}$ $y=\frac{24}{31}$
  
• D. x=1 y=0

Answer 1

The correct option is A $x=\frac{24}{31}$ $y=\frac{36}{31}$


$8x+5y=12$...........(1)
$3x-2y=0$..............(2)
Multiplying by 8 in (2) and 3 in (1), we get
$24x+15y=36$
$24x-16y=0$
_____________
$31y=36\Rightarrow y=\frac{36}{31}$

Substituting $y=\frac{36}{31}$ in equation (2), we get
$3x-2y=0$
$\Rightarrow 3x-2\left(\frac{36}{31}\right)=0\Rightarrow 3x-\frac{72}{31}=0$

$\Rightarrow 3x=\frac{72}{31}\Rightarrow x=\frac{72}{31\times 3}$
$\therefore x=\frac{24}{31}$