Solve the system of equations.
\[
\left\{\begin{array}{r}
8 x-y=-11 \\
y=-8 x
\end{array}\right.
\]

Answer

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Answer

The solution to the system of equations is \(x = -\frac{11}{16}\) and \(y = \frac{11}{2}\)

Steps

Step 1 ：Solve the second equation for y: \(y = -8x\)

Step 2 ：Substitute \(y = -8x\) into the first equation: \(8x - (-8x) = -11\)

Step 3 ：Simplify the equation: \(8x + 8x = -11\)

Step 4 ：Combine like terms: \(16x = -11\)

Step 5 ：Solve for x: \(x = -\frac{11}{16}\)

Step 6 ：Substitute \(x = -\frac{11}{16}\) into the second equation to find y: \(y = -8(-\frac{11}{16})\)

Step 7 ：Simplify the equation: \(y = \frac{88}{16}\)

Step 8 ：Simplify the fraction: \(y = \frac{11}{2}\)

Step 9 ：The solution to the system of equations is \(x = -\frac{11}{16}\) and \(y = \frac{11}{2}\)