Question

The pair of linear equations $x+y=3,2x+5y=12$ has a unique solution $x=x_1,y=y_1$ then value of $x_1$ is?

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

The correct option is A $1$

Given equations are
$x+y=3$
$2x+5y=12$
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 equations, we get
$x_1+y_1=3$ ....$\left(1\right)$
$2x_1+5y_1=12$ ....$\left(2\right)$
From equation $\left(1\right)$, we have
$y_1=3-x_1$
Putting the value of $y_1$ in equation $\left(2\right)$,
$\Rightarrow 2x_1+5(3-x_1)=12$
$\Rightarrow 2x_1+15-5x_1=12$
$\Rightarrow 2x_1-5x_1=12-15$
$\Rightarrow -3x_1=-3$
$\Rightarrow x_1=\frac{-3}{-3}$
$\Rightarrow x_1=1$