To determine if \((-5, 0.5)\) is a solution of the given system of equations, we will substitute \(x = -5\) and \(y = 0.5\) into each equation.
First Equation:
\[ x - 4y = -7 \]
Substituting \((-5, 0.5)\): \[ -5 - 4(0.5) = -7 \] Calculating: \[ -5 - 2 = -7 \] This simplifies to: \[ -7 = -7 \quad \text{(True)} \]
Second Equation:
\[ 0.2x + 2y = 0 \]
Substituting \((-5, 0.5)\): \[ 0.2(-5) + 2(0.5) = 0 \] Calculating: \[ -1 + 1 = 0 \] This simplifies to: \[ 0 = 0 \quad \text{(True)} \]
Conclusion:
Both equations are satisfied, therefore \((-5, 0.5)\) is a solution of the system.