Final answer:
By substituting y = 9 + 3x into the equation 2 + x = 3 + y, we find that the solution to the system of equations is x = -5 and y = -6.
Step-by-step explanation:
The provided equation is 2 + x = 3 + y. We also have a function y = 9 + 3x, which represents a line on a graph where b is the y-intercept and m is the slope of the line. To solve for x and y, we must substitute the second equation into the first one.
Let's proceed with the substitution:
- 2 + x = 3 + (9 + 3x)
- 2 + x = 3 + 9 + 3x
- 2 + x = 12 + 3x
- 2 = 12 + 2x
- -10 = 2x
- x = -5
Now that we have x, we can solve for y:
- y = 9 + 3(-5)
- y = 9 - 15
- y = -6
Therefore, the solution to the system of equations where 2 + x = 3 + y and y = 9 + 3x is x = -5 and y = -6.