Final answer:
The solution to the system of equations y = 3x + 19 and y = 5x + 33 is found by setting them equal to each other and solving for x, which is -7, then plugging x back into either equation to solve for y, which is -2. Therefore, the solution is (x, y) = (-7, -2).
Step-by-step explanation:
When solving the system of equations given by y = 3x + 19 and y = 5x + 33, you can use either substitution or elimination. Since they are both in y = mx + b form, it is straightforward to use substitution.
Set the two equations equal to each other because they both equal y:
3x + 19 = 5x + 33
Solve for x:
19 - 33 = 5x - 3x
-14 = 2x
x = -7
Now, substitute x back into either of the original equations to solve for y:
y = 3(-7) + 19
y = -21 + 19
y = -2
Therefore, the solution to the system of equations is (x, y) = (-7, -2).