Answer: The required value of variable x is 3.
Step-by-step explanation: We are given to find the value of the variable x in the solution to the following system of equations :
\(4x-3y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x-4y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\)
In order to find the value of x, we need to eliminate y from both the equations.
Multiplying equation (i) by 4 and equation (ii) by 3, we have
\(4(4x-3y)=4\times 3\\\\\Rightarrow 16x-12y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\\\3(5x-4y)=3\times3\\\\\Rightarrow 15x-12y=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\)
Subtracting equation (iv) from equation (iii), we get
\((16x-12y)-(15x-12y)=12-9\\\\\Rightarrow x=3.\)
Thus, the required value of variable x is 3.
