Question

The pair of linear equations $3x-5y+1=0,2x-y+3=0$ has a unique solution $x=x_1,y=y_1$ then $y_1=$

• A. $1$
• B. $-1$
• C. $-2$
• D. $-4$

Answer 1

Answer: (B)

$-1$

Given equations are
$3x-5y+1=0$
$2x-y+3=0$
Since, the system has unique solution at $x=x_1$ and $y=y_1$
That means the lines intersect at only one point $(x_1,y_1)$
By putting $x=x_1$ and $y=y_1$ in given equations
$3x_1-5y_1+1=0$ .....(1)
$2x_1-y_1+3=0$ .....(2)
From equation(2), we have
$y_1=2x_1+3$ .....(3)
Putting the value of $y_1$ in equation(1)
$3x_1-5(2x_1+3)+1=0$
$\Rightarrow 3x_1-10x_1-15+1=0$
$\Rightarrow -7x_1-14=0$
$\Rightarrow -7x_1=14$
$\Rightarrow x_1=-2$
Put this value in equation (3), we get
$y_1=2(-2)+3$
$y_1=-1$