Question

The linear equation \[2y - 3 = 0,\]represented as \[ax + by + c = 0,\]has.
A.A unique solution
B.Infinitely many solution
C.Two solutions
D.No solution

Answer 1

Hint: First write the linear equation for all variables. Now write the condition of x. Now you have a 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 both sides. By this you get condition on y. From these both conditions find the point or solution. That is the required result.

Complete step-by-step answer:
The given equation in the question, can be written in form:
\[2y + 0x - 3 = 0\]
As you can see, the coefficient of x is 0. So, we can say:
The value of x 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:
\[x = m;{\rm{ m}} \in {\rm{ real number}}{\rm{.}}\]
By removing x, we get the equation in the form of:
\[2y - 3 = 0\]
The value of constant on left hand side is -3 to cancel that term we need to add it on both sides, by adding 3 on both sides, we get the equation as:
\[2y - 3 + 3 = 3\]
By simplifying the above equation, we get it in the form:
\[2y = 3\]
By dividing with 2 on both sides, we get it as:
\[\dfrac{{2y}}{2} = \dfrac{3}{2}\]
By simplifying the above equation, we get it in the form:
\[y = \dfrac{3}{2}\]
As x can be any real number, we say the solution of this linear equation has x as any variable. From options let it be as m. So, solution of this equation is given by:
\[\left( {m,\dfrac{3}{2}} \right)\]
As m can be any real value we get infinite solutions.
Therefore, option (b) is the correct answer.

Note: Be careful while stating the condition on x. Because it is the point which gives us the result. While finding the value of y 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.