Final answer:
To find a solution for the given equations 2y-2x=12x² and y²=36, we can use the substitution method. From the algebraic calculations, we can determine that there is no one solution for these equations.
Step-by-step explanation:
In order to find a solution for the given equations 2y-2x=12x² and y²=36, we will use the substitution method. Let's solve the first equation for y:
2y-2x=12x²
2y = 12x² + 2x
y = 6x² + x
Now substitute this value of y in the second equation:
(6x² + x)² = 36
36x⁴ + 12x³ + x² = 36
36x⁴ + 12x³ + x² - 36 = 0
This is a quartic equation. In order to find the solutions, we can use factoring, graphing, or numerical methods.
Therefore, there is no one solution that can be obtained algebraically for the given equations.
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