Answer
\[x=-4,\ y=\frac{5}{4}\]
Work Step by Step
The equation \[x+8y=6\]can be written as follows:
\[\begin{align}
& x+8y=6 \\
& x=6-8y
\end{align}\]
Substitute\[x=6-8y\]in the equation\[2x+4y=-3\], to get:
\[\begin{align}
& 2\left( 6-8y \right)+4y=-3 \\
& 12-16y+4y=-3 \\
& -12y=-15 \\
& y=\frac{5}{4}
\end{align}\]
Substitute \[y=\frac{5}{4}\]in\[x=6-8y\], to get:
\[\begin{align}
& x=6-8\left( \frac{5}{4} \right) \\
& =6-10 \\
& =-4
\end{align}\]
Put\[x=-4\]and \[y=\frac{5}{4}\]in any of the given equations to check the solution:
\[\begin{align}
& 2\left( -4 \right)+4\left( \frac{5}{4} \right)=-3 \\
& -8+5=-3 \\
& -3=-3
\end{align}\]
Since, RHS\[=\]LHS, it implies the solution is correct.
Now check x = -4, y =5/4 with the equation x + 8y = 6 too.
-4 + 8(5/4) = 6
-4 + 10 = 6
6 = 6.So, its solution satisfies both the equations.
