Question

Solve the following pair of linear equations by substitution method:
$2x+3y=13$
$4x-y=5$

• A. $x=3,y=2$
• B. $x=2,y=3$
• C. $x=4,y=3$
• D. $x=2,y=2$

Answer 1

The correct option is B $x=2,y=3$

$2x+3y=13$............(1)
$4x-y=5$............(2)
from equation (2),
$4x-y=5\Rightarrow 4x-5=y$
Substituting $y=4x-5$ in equation (1), we get:
$2x+3y=13\Rightarrow 2x+3(4x-5)=13$
$2x+12x-15=13\Rightarrow 14x=13+15$
$14x=28\Rightarrow x=\frac{28}{14}$
$\therefore x=2$
Substituting the value of x =2 in equation (3), we get:
$y=4x-5$
$y=4\left(2\right)-5=8-5=3$
$\therefore y=3$
Hence the solution is x=2, y=3