\( \left. \begin{array} { c } { a + b = 0,45 \ldots 41 } \\ { - 3 a + b = - 0,15 \ldots 181 } \\ { a = ? } \\ { b = ? } \end{array} \right. \)

To solve the system of equations, we can rewrite the first equation as \( b = 0.45 - a \). Next, we'll substitute this expression for \( b \) into the second equation: \[ -3a + (0.45 - a) = -0.15 \] Simplifying this, we have: \[ -3a + 0.45 - a = -0.15 \] Combining like terms gives: \[ -4a + 0.45 = -0.15 \] Subtracting \( 0.45 \) from both sides results in: \[ -4a = -0.15 - 0.45 \] Which simplifies to: \[ -4a = -0.60 \] Dividing both sides by -4: \[ a = 0.15 \] Now, substituting \( a \) back into the expression for \( b \): \[ b = 0.45 - 0.15 = 0.30 \] So, the solution is \( a = 0.15 \) and \( b = 0.30 \).