Question

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

Answer 1

Hint: 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.