what is x and y if 5x + 12y = 1.34 and 8x + 2y =0.96
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MathBot Answer:
The system of linear equations has exactly one solution.
\[x = \frac{221}{2150}\]
\[y = \frac{74}{1075}\]
Solve \(5 x + 12 y = \frac{67}{50}\) for \(x\). \[x = \frac{67}{250} - \frac{12 y}{5}\]
Substitute \(\frac{67}{250} - \frac{12 y}{5}\) for \(x\) in \(8 x + 2 y = \frac{24}{25}\) and simplify. $$\begin{aligned}8 x + 2 y &= \frac{24}{25} \\ 8 \left(\frac{67}{250} - \frac{12 y}{5}\right) + 2 y &= \frac{24}{25} \\ y &= \frac{74}{1075} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{67}{250} - \frac{12 y}{5} \\ x &= - \frac{12 \cdot 74}{5 \cdot 1075} + \frac{67}{250} \\ x &= \frac{221}{2150}\end{aligned}$$