3x + 2y = -2 , 4x + 6y = -4 find x and y
You asked:
Given \( 3 x + 2 y = -2 \), \( 4 x + 6 y = -4 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = - \frac{2}{5}\]
\[y = - \frac{2}{5}\]
Solve \(3 x + 2 y = -2\) for \(x\). \[x = - \frac{2 y}{3} - \frac{2}{3}\]
Substitute \(- \frac{2 y}{3} - \frac{2}{3}\) for \(x\) in \(4 x + 6 y = -4\) and simplify. $$\begin{aligned}4 x + 6 y &= -4 \\ 4 \left(- \frac{2 y}{3} - \frac{2}{3}\right) + 6 y &= -4 \\ y &= - \frac{2}{5} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= - \frac{2 y}{3} - \frac{2}{3} \\ x &= - \frac{2}{3} - - \frac{4}{3 \cdot 5} \\ x &= - \frac{2}{5}\end{aligned}$$