3x+4y=470
5x+6y=730
evaluate x and y
You asked:
Given \( 3 x + 4 y = 470 \), \( 5 x + 6 y = 730 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = 50 \), \( y = 80 \).
\[x = 50\]
\[y = 80\]
Solve \(3 x + 4 y = 470\) for \(x\). \[x = \frac{470}{3} - \frac{4 y}{3}\]
Substitute \(\frac{470}{3} - \frac{4 y}{3}\) for \(x\) in \(5 x + 6 y = 730\) and simplify. $$\begin{aligned}5 x + 6 y &= 730 \\ 5 \left(\frac{470}{3} - \frac{4 y}{3}\right) + 6 y &= 730 \\ y &= 80 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{470}{3} - \frac{4 y}{3} \\ x &= \frac{470}{3} - \frac{4 \cdot 80}{3} \\ x &= 50\end{aligned}$$