Answer :
[tex]\text{The solution is } x = \frac{-14}{11} \text{ and } y = \frac{62}{11}[/tex]
Solution:
Given system of equations are:
8x + 5y = 18 ------- eqn 1
6x + y = -2 -------- eqn 2
Multiply eqn 2 by -5
-30x -5y = 10 ----- eqn 3
Add eqn 1 and eqn 3 so that y terms gets eliminated
8x + 5y = 18
-30x -5y = 10
( + ) --------------
-22x = 28
Divide both sides by -22
[tex]x = \frac{28}{-22}\\\\x = \frac{-14}{11}[/tex]
Substitute the x value in eqn 1
[tex]8(\frac{-14}{11}) + 5y = 18\\\\\frac{-112}{11} + 5y = 18\\\\5y = 18 + \frac{112}{11}\\\\5y = \frac{310}{11}\\\\y = \frac{62}{11}[/tex]
[tex]\text{Thus the solution is } x = \frac{-14}{11} \text{ and } y = \frac{62}{11}[/tex]