8x+4y=64
4x+8y=92
solve for x and y
You asked:
Given \( 8 x + 4 y = 64 \), \( 4 x + 8 y = 92 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = 3 \), \( y = 10 \).
\[x = 3\]
\[y = 10\]
Solve \(8 x + 4 y = 64\) for \(x\). \[x = 8 - \frac{y}{2}\]
Substitute \(8 - \frac{y}{2}\) for \(x\) in \(4 x + 8 y = 92\) and simplify. $$\begin{aligned}4 x + 8 y &= 92 \\ 4 \left(8 - \frac{y}{2}\right) + 8 y &= 92 \\ y &= 10 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 8 - \frac{y}{2} \\ x &= 8 - \frac{10}{2} \\ x &= 3\end{aligned}$$