Answer: (x, y) = (-2, 3) is the required solution.
Step-by-step explanation: We are given to find the solution to the following system of linear equations:
[tex]4x+5y=7~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-2y=-12~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 3 and equation (ii) by 4, we have
[tex]12x+15y=21~~~~~~~~~~~~~~~~~(iii)\\\\12x-8y=-48~~~~~~~~~~~~~~~~(iv)[/tex]
Subtracting equation (iv) from equation (iii), we get
[tex](12x+15y)-(12x-8y)=21-(-48)\\\\\Rightarrow 12x+15y-12x+8y=21+48\\\\\Rightarrow 23y=69\\\\\Rightarrow y=3,[/tex]
and from equation (i), we get
[tex]4x+5\times 3=7\\\\\Rightarrow 4x+15=7\\\\\Rightarrow 4x=-8\\\\\Rightarrow x=-2.[/tex]
Therefore, the solution to the given system is x = - 2, y = 3.
Thus, (x, y) = (-2, 3) is the required solution.
