What does it mean for a point to be a solution to a linear equation?

A point \((x, y)\) is a solution to a linear equation if, when you substitute the \(x\) value of the point into the equation, the resulting \(y\) value matches the given \(y\) value in the point.

In your example, you claim that the point \((2, 5)\) is a solution to the equation \(y = 2x + 3\). To check your claim, follow these steps:

1. Identify the \(x\) value: In the point \((2, 5)\), the \(x\) value is \(2\).

2. Substitute \(x\) into the equation: Replace \(x\) in the equation \(y = 2x + 3\) with \(2\):

   \[ y = 2(2) + 3 \]

3. Calculate the right side:

   \[ y = 4 + 3 = 7 \]

4. Compare with the given \(y\) value: In the point \((2, 5)\), the \(y\) value is \(5\), but our calculation shows \(y = 7\).

Since \(5 \neq 7\), the point \((2, 5)\) is not a solution to the equation \(y = 2x + 3\). This means that \((2, 5)\) does not satisfy the equation.