x+3y=12.7
x+y=7.1
find x and y
You asked:
Given \( x + 3 y = 12.7 \), \( x + y = 7.1 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = \frac{43}{10} \), \( y = \frac{14}{5} \).
\[x = \frac{43}{10}\]
\[y = \frac{14}{5}\]
Solve \(x + 3 y = \frac{127}{10}\) for \(x\). \[x = \frac{127}{10} - 3 y\]
Substitute \(\frac{127}{10} - 3 y\) for \(x\) in \(x + y = \frac{71}{10}\) and simplify. $$\begin{aligned}x + y &= \frac{71}{10} \\ \left(\frac{127}{10} - 3 y\right) + y &= \frac{71}{10} \\ y &= \frac{14}{5} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{127}{10} - 3 y \\ x &= \frac{127}{10} - 3 \cdot \frac{14}{5} \\ x &= \frac{43}{10}\end{aligned}$$