Answer: The required solution is x = 3, y = -8.
Step-by-step explanation: We are given to solve the following system of linear equations :
[tex]x+2y=-13~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\12x+5y=-4~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]x+2y=-13\\\\\Rightarrow x=-13-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~`(iii)[/tex]
Substituting the value of x from equation (iii) in equation (ii), we get
[tex]12x+5y=-4\\\\\Rightarrow 12(-13-2y)+5y=-4\\\\\Rightarrow -156-24y+5y=-4\\\\\Rightarrow -19y=-4+156\\\\\Rightarrow -19y=152\\\\\Rightarrow y=-\dfrac{152}{19}\\\\\Rightarrow y=-8.[/tex]
Equation (iii) implies that
[tex]x=-13-2\times(-8)=-13+16=3.[/tex]
Thus, the required solution is x = 3, y = -8.
