Question

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

For example, if I say, "(2, 4) is a solution to the equation y = 2x + 3 how could you check my claim?

Answer 1

For a point \((x, y)\) to be a solution to a linear equation, it means that when you substitute the \(x\) value of the point into the equation, the resulting \(y\) value must be equal to the \(y\) value of the point.

In your example, the point \((2, 4)\) is claimed to be a solution to the equation \(y = 2x + 3\).

To check this claim, follow these steps:

1. Substitute the \(x\) value of the point into the equation. Here, \(x = 2\).

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

2. Calculate the right side of the equation:

\[
y = 4 + 3
\]

\[
y = 7
\]

3. Now compare the calculated \(y\) value (which is 7) to the \(y\) value of the point (which is 4).

Since 7 is not equal to 4, the point \((2, 4)\) is **not** a solution to the equation \(y = 2x + 3\).

In summary, to verify if a point is a solution to a linear equation, plug in its \(x\) value into the equation and check if the resulting \(y\) value matches the point's \(y\) coordinate.