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The question asks whether the point \((5, 2)\) is a solution to the following system of equations:

\[
y = \frac{2}{5}x + 8
\]
\[
y = \frac{3}{5}x - 5
\]

To determine if \((5, 2)\) is a solution, we can substitute \(x = 5\) and \(y = 2\) into both equations and check if they satisfy both.

### First equation:
\[
y = \frac{2}{5}x + 8
\]
Substituting \(x = 5\) and \(y = 2\):
\[
2 = \frac{2}{5}(5) + 8
\]
\[
2 = 2 + 8 \quad \text{(which simplifies to)} \quad 2 = 10
\]
This is false, so the point \((5, 2)\) does **not** satisfy the first equation.

Since it fails the first equation, the point \((5, 2)\) is not a solution to the system.

The answer is **False**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you solve a system of equations graphically?
2. What is the significance of a solution in a system of linear equations?
3. Can a system of equations have no solution? When does that occur?
4. How do you check if a point satisfies a quadratic system of equations?
5. What methods are available to solve systems of linear equations (e.g., substitution, elimination)?

**Tip**: When checking if a point is a solution to a system of equations, always substitute the point into *both* equations and ensure both are satisfied.

True or False: (5, 2) is a solution to the following system? y = (2/5)x + 8, y = (3/5)x - 5

Check whether the point (5, 2) satisfies the system of linear equations: y = (2/5)x + 8 and y = (3/5)x - 5. This problem involves substituting the point into both equations and solving. Suitable for students in Grades 8-10.

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