Answer:
(x, y) = (-3, -4).
Step by step explanation:
To solve the system of equations:
y = 3x + 5 ... (1)
x + y = -7 ... (2)
We can use the substitution method or the elimination method. Here's how to use the substitution method:
From equation (2), we can solve for y in terms of x:
y = -x - 7
We can then substitute this expression for y in equation (1):
x - 7 = 3x + 5
Simplifying this equation, we get:
4x = -12
Dividing both sides by 4, we get:
x = -3
Substituting this value of x in equation (2), we can solve for y:
-3 + y = -7
y = -4
Therefore, the solution to the system of equations is x = -3 and y = -4. We can check that this is the correct solution by verifying that both equations are satisfied when x = -3 and y = -4:
y = 3x + 5 --> -4 = 3(-3) + 5 --> -4 = -4 (true)
x + y = -7 --> (-3) + (-4) = -7 --> -7 = -7 (true)
Therefore, the solution is (x, y) = (-3, -4).