Question

Find the value of ‘$m$’, if $( - m,3)$ is a solution of equation $4x + 9y - 3 = 0$ .

Answer 1

It is given that $( - m,3)$ is a solution of equation $4x + 9y - 3 = 0$, it means that $( - m,3)$ satisfies the equation of line $4x + 9y - 3 = 0$. We will put the point $( - m,3)$ in $4x + 9y - 3 = 0$ to obtain an equation in $m$. Solving this obtained equation will give the value of $m$.

Complete step by step answer:
The solution of an equation, also known as the root of the equation, is any value or set of values that can be substituted into the equation to make it a true statement.
We have a point $( - m,3)$ which is a solution of the equation $4x + 9y - 3 = 0$. It means that on putting $( - m,3)$ in $4x + 9y - 3$, we will get the result as zero i.e., value of $\left[ {4 \times \left( { - m} \right) + \left( {9 \times 3} \right) - 3} \right]$ will be equal to zero.
Putting $- m$ in the place of $x$ and $3$ in the place of $y$ i.e., $x = - m$ and $y = 3$ in equation $4x + 9y - 3 = 0$, we get
$\Rightarrow 4 \times \left( { - m} \right) + \left( {9 \times 3} \right) - 3 = 0$
On solving the above equation, we get
$\Rightarrow - 4m + 27 - 3 = 0$
On simplification,
$\Rightarrow - 4m + 24 = 0$
Taking $24$ from left hand side to right hand side, we get
$\Rightarrow - 4m = - 24$
Eliminating minus sign from both the sides, we get
$\Rightarrow 4m = 24$
Dividing both the sides by $4$, we get
$\Rightarrow m = \dfrac{{24}}{4}$
0n simplifying,
$\Rightarrow m = 6$
Therefore, the value of ‘$m$’ if $( - m,3)$ is a solution of equation $4x + 9y - 3 = 0$ is $6$.

Note:
$( - m,3)$ is one of the solutions of the equation $4x + 9y - 3 = 0$. There will be infinite numbers of points which will be the solution of this equation. One thing common in all the points satisfying the equation $4x + 9y - 3 = 0$ is that they all lie on the same straight line. Plotting every point which is the solution of the equation $4x + 9y - 3 = 0$ will give a straight line on which all these points will lie.