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The solutions to the simultaneous equations are as follows:

1. \( x = \frac{-13}{2} - \frac{9\sqrt{2}}{2}, \quad y = -9\sqrt{2} - 10 \)
2. \( x = \frac{-13}{2} + \frac{9\sqrt{2}}{2}, \quad y = -10 + 9\sqrt{2} \)

Let me convert these into decimal form, as requested for 2 decimal places.The decimal solutions to the simultaneous equations (rounded to 2 decimal places) are:

1. \( x = -13.00, \quad y = -23.00 \)
2. \( x = -0.14, \quad y = 2.70 \)

Would you like further details on how these solutions were derived or have any questions?

Here are some related questions to expand your understanding:
1. What are simultaneous equations and why are they important?
2. How would these equations change if \( y = 2x + 5 \) instead of \( y = 2x + 3 \)?
3. What are the methods to solve non-linear simultaneous equations like these?
4. Why do we sometimes get multiple solutions in systems like this?
5. How can we verify the solutions graphically?

**Tip:** Always substitute your solutions back into the original equations to ensure they satisfy both equations!

Solve these simultaneous equations: y = 2x + 3, 40x + y^2 = 2. If any of your answers are decimals, give them to 2 d.p.

Learn how to solve the simultaneous equations y = 2x + 3 and 40x + y^2 = 2 using substitution and quadratic methods. Find the decimal solutions to 2 decimal places. This solution is ideal for students in Grades 10-12 looking to deepen their understanding of non-linear systems.

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