if x+5y=16 and x=-3y, then y=
You asked:
Given the following equations: \[\begin{aligned}x + 5 y &= 16\\ x &= -\left( 3 y \right)\end{aligned}\] Evaluate \(y\).
MathBot Answer:
The system of linear equations has exactly one solution.
\[y = 8\]
Solve \(x + 5 y = 16\) for \(x\). \[x = 16 - 5 y\]
Substitute \(16 - 5 y\) for \(x\) in \(x = - 3 y\) and simplify. $$\begin{aligned}x &= - 3 y \\ \left(16 - 5 y\right) &= - 3 y \\ y &= 8 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 16 - 5 y \\ x &= 16 - 5 \cdot 8 \\ x &= -24\end{aligned}$$