To solve the equations for x and y, we start with the given equation: 7y + 3 = 2x^2 + 14 + 4y – 2 + 3x.
First, we need to simplify the equation. Reorganizing terms, we get:
1. Move all terms involving y to one side and those involving x to the other side:
7y – 4y = 2x^2 + 3x + 14 – 3 + 2
2. This simplifies to:
3y = 2x^2 + 3x + 13
3. Next, divide everything by 3:
y = (2/3)x^2 + x + (13/3)
Now we have y expressed in terms of x.
To find specific solutions for x and y, you can select values for x and then calculate the corresponding y for each. If we want integer solutions, we can test integer values for x:
Example:
If x = 1:
y = (2/3)(1)² + (1) + (13/3) = (2/3) + (3/3) + (13/3) = (2 + 3 + 13) / 3 = 18/3 = 6
If x = 2:
y = (2/3)(2)² + (2) + (13/3) = (8/3) + (3/3) + (13/3) = (8 + 3 + 13) / 3 = 24/3 = 8
This way, you can create a table with values for x and corresponding values for y:
x | y
1 | 6
2 | 8
In conclusion, you can express y in terms of x and then choose x values to find the corresponding y values.