Answer: The required solution is x = -4 and y = -1.
Step-by-step explanation: We are given to solve the following system of equations by the method of Elimination :
[tex]x+2y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+8y=-20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 3 , we have
[tex]3(x+2y)=-6\times3\\\\\Rightarrow 3x+6y=-18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (iii) from equation (ii), we get
[tex](3x+8y)-(3x+6y)=-20-(-18)\\\\\Rightarrow 2y=-20+18\\\\\Rightarrow 2y=-2\\\\\Rightarrow y=-\dfrac{2}{2}\\\\\Rightarrow y=-1.[/tex]
From equation (i), we get
[tex]x+2\times(-1)=-6\\\\\Rightarrow x-2=-6\\\\\Rightarrow x=-6+2\\\\\Rightarrow x=-4.[/tex]
Thus, the required solution is x = -4 and y = -1.
