Answer: The required solution is (x, y) = (5, -2).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]2x+5y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-4y=23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]2x+5y=0\\\\\Rightarrow 2x=-5y\\\\\Rightarrow x=-\dfrac{5}{2}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of x from equation (iii) in equation (ii), we get
[tex]3\times\left(-\dfrac{5}{2}y\right)-4y=23\\\\\\\Rightarrow -15y-8y=46\\\\\Rightarrow -23y=46\\\\\Rightarrow y=-\dfrac{46}{23}\\\\\Rightarrow y=-2.[/tex]
From equation (iii), we get
[tex]x=-\dfrac{5}{2}\times(-2)=5.[/tex]
Thus, the required solution is (x, y) = (5, -2).
