The term "solution" generally refers to an answer to a problem or a means to resolve an equation. In the context of equations, a solution is a set of values that satisfy the equation when substituted in.
For a point to be a solution to a linear equation, it means that when you substitute the coordinates of the point into the equation, the equation holds true.
For your specific example, you claim that the point (2, 5) is a solution to the equation \( y = 2x + 3 \). To check this, you would do the following:
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Identify the coordinates of the point: \( x = 2 \) and \( y = 5 \).
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Substitute \( x = 2 \) into the right side of the equation:
\[ y = 2(2) + 3 \]
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Calculate the right side:
\[ y = 4 + 3 = 7 \]
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Now compare the calculated value of \( y \) (which is 7) with the \( y \)-coordinate of the point (which is 5). Since \( 7 \neq 5 \), the point (2, 5) does not satisfy the equation.
Therefore, (2, 5) is not a solution to the equation \( y = 2x + 3 \).
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