Answer:
(x, y) = (-7, -2).
Explanation:
To solve the system of equations:
y = 3x + 19
y = 5x + 33
We can use the substitution method, which involves solving one equation for one variable and substituting that expression into the other equation. Then we can solve for the remaining variable.
From the first equation, we can solve for y in terms of x:
y = 3x + 19
From the second equation, we can solve for y in terms of x:
y = 5x + 33
Now we can substitute the expression for y from the first equation into the second equation:
3x + 19 = 5x + 33
Simplifying this equation by subtracting 3x from both sides:
19 = 2x + 33
Subtracting 33 from both sides:
-14 = 2x
Dividing both sides by 2:
x = -7
Now that we have the value of x, we can substitute it back into either equation to find the value of y:
y = 3x + 19
y = 3(-7) + 19
y = -21 + 19
y = -2
The solution to the system of equations is (x, y) = (-7, -2).