Answer
\[x=-7,\ y=1\]
Work Step by Step
The equation \[-x+3y=10\]can be written as follows:
\[\begin{align}
& -x+3y=10 \\
& -x=10-3y \\
& x=3y-10
\end{align}\]
Substitute\[x=3y-10\]in the equation\[2x+8y=-6\], to get:
\[\begin{align}
& 2\left( 3y-10 \right)+8y=-6 \\
& 6y-20+8y=-6 \\
& 14y=14 \\
& y=1
\end{align}\]
Substitute \[y=1\]in\[x=3y-10\], to get:
\[\begin{align}
& x=3\left( 1 \right)-10 \\
& =3-10 \\
& =-7
\end{align}\]
Put\[x=-7\]and \[y=1\]in any of the given equations to check the solution:
\[\begin{align}
& 2\left( -7 \right)+8\left( 1 \right)=-6 \\
& -14+8=-6 \\
& -6=-6
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Similarly check with –x + 3y = 10 also.
-(-7) +3(1) = 10
7 +3 = 10
10 = 10
So, (-7, 1) is the correct solution to this system of equations.
