Solve the equation.
$1+3=-y+9$
The objective is to solve the linear equation \(1 + 3 = -y + 9\) for the variable \(y\) and identify which of the given options matches the result. First, simplify the left side of the equation: \(1 + 3 = 4\). The equation becomes \(4 = -y + 9\). To isolate \(y\), subtract 9 from both sides, yielding \(4 - 9 = -y\), which simplifies to \(-5 = -y\). Multiplying both sides by -1 gives \(y = 5\).
Upon reviewing the provided options (\(y=1, y=3, y=6, y=9\)) and the calculated result \(y = 5\), it appears there is no match among the given choices. Given that the equation is \(1 + 3 = -y + 9\), the solution is mathematically determined to be \(y = 5\). Since this value is not provided as an option, the correct solution remains \(y = 5\).
In real-life scenarios, solving linear equations like this is fundamental for budgeting and resource management. For instance, if you have a budget of \(\$9\) and you know you spent some money (\(y\)) and need to ensure your remaining amount matches a total of \(1+3 = \$4\), you would solve \(9 - y = 4\) to find out how much you spent. In this case, you would have spent \(y = \$5\). This demonstrates how algebraic equations allow us to track and verify our financial or logical constraints in daily activities.