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