A point \((x, y)\) is said to be a solution to a linear equation if, when the coordinates of the point are substituted into the equation, the equation holds true. This means that the left-hand side of the equation should equal the right-hand side when you plug in the values of \(x\) and \(y\).
In your example, the point \( (2, 5) \) is claimed to be a solution to the equation \( y = 2x + 3 \). To check this claim, follow these steps:
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Identify the values of \(x\) and \(y\) from the point. Here, \(x = 2\) and \(y = 5\).
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Substitute \(x\) into the equation \(y = 2x + 3\): \[ y = 2(2) + 3 \]
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Calculate the right-hand side: \[ y = 4 + 3 = 7 \]
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Compare the calculated value of \(y\) with the \(y\) from the point \( (2, 5) \). We found \(y = 7\) from the equation, but the point gives \(y = 5\).
Since \(7 \neq 5\), the point \( (2, 5) \) is not a solution to the equation \( y = 2x + 3\).
In summary, to verify if a point is a solution to a linear equation, substitute the \(x\) value into the equation and check if the resulting \(y\) value matches the \(y\) coordinate of the point. If they match, the point is a solution; if they do not, it is not a solution.