Question

Any solution of the linear equation $2x+0y+9=0$ in two variables is of the form:
(a) $\left( -\dfrac{9}{2},m \right)$
(b) $\left( n,-\dfrac{9}{2} \right)$
(c) $\left( 0,-\dfrac{9}{2} \right)$
(d) $\left( -9,0 \right)$

Answer 1

Hint: First write the linear equation with all variables. Now write the conditions of y. Now you have an one variable equation. Find the value of the constant on the left-hand side. Subtract the value of constant on both sides of the equation. Now you get a variable on the left-hand side and constant on the right-hand side. Now find the coefficient of variable on the left-hand side and divide with the coefficient on both sides. By this you get a condition on x. From these both conditions find the point or solution. That is the required result.

Complete step-by-step solution -
The given equation in the question, can be written in form:
$2x+0y+9=0$
As you can see, the coefficient of y is 0. So, we can say: The value of y may be any real number it does not matter to the solution because its effect is nullified by the coefficient being 0 in the given equation. By the above explanation, we can say the value of y as: y=m; $m\in $ real number.
So, by removing the y, we get the equation in the form:
$2x+9=0$
The value of constant on the left-hand side is 9. To cancel out that term we must subtract it on both sides. By subtracting 9 on both sides, we get:
$2x+9-9=-9$
By simplifying the above equation, we get it in form:
$2x=-9$
By dividing with 2 on both sides, we get it as:
$\dfrac{2x}{2}=\dfrac{-9}{2}$
By simplifying the above equation, we get it as:
$x=\dfrac{-9}{2}$
As y can be any real number, we say the solution of this linear equation has y as any variable. From options let it be as m. so, solution of this equation is given by:
$\left( -\dfrac{9}{2},m \right)$
Therefore, option (a) is the correct answer.

Note: Be careful while stating any condition. Because it is the point which gives us the results while finding the value of x, any operation applied on the left-hand side must be applied on the right-hand side also. Don’t forget this step. If you forget you may lead to the wrong answer.