Question

$x=2,y=-1$ is a solution of the linear equation
(a) $x+2y=0$
(b) $x+2y=4$
(c) $2x+y=0$
(d) $2x+y=5$

Answer 1

Given ordered pair $x=2,y=-1$
To verify whether the given order pair is a solution of given equation, we need to verify whether the order pair satisfies the equation or not.

(i) Consider the equation $x+2y=0$
Substitute $x=2,y=-1$ in above equation, we get
$2+2(-1)=0$
$\Rightarrow 2-2=0$
$\Rightarrow 0=0$ true
The point $x=2,y=-1$ satisfies the equation $x+2y=0$.
Hence, the point $x=2,y=-1$ is solution for the equation $x+2y=0$.
(ii) Consider the equation $x+2y=4$
Substitute $x=2,y=-1$ in above equation, we get
$\Rightarrow 2+2(-1)=4$
$\Rightarrow 2-2=4$
$\Rightarrow 0=4$ is false.
Thus, the given order pair does not satisfies the given equation.
Hence, the point $x=2,y=-1$ is not a solution for the equation $x+2y=4$.

(iii) Consider the equation $2x+y=0$
Substitute $x=2,y=-1$ in above equation, we get
$\Rightarrow 2\left(2\right)+(-1)=0$
$\Rightarrow 4-1=0$
$\Rightarrow 3=0$ is false.
Hence, the point $x=2,y=-1$ is not a solution for the equation $2x+y=0$

(iv) The given equation $2x+y=5$
Substitute $x=2,y=-1$ in above equation, we get
$\Rightarrow 2x+y=5$
$\Rightarrow 2\left(2\right)+(-1)=5$
$\Rightarrow 4-1=5$
$\Rightarrow 3=5$ is false.
Hence, the point $2x+y=5$ is not a solution for the equation $2x+y=5$.

Therefore, the correct answer is (a).