Answer: (x, y) = (-2, 4).
Explanation:
To solve the system of equations y=x+6 and y+2x=0, we can use the substitution method. We can solve one of the equations for one variable and substitute the result into the other equation. Let’s solve the first equation for y:
y = x + 6
Now we can substitute this expression for y in the second equation:
(x + 6) + 2x = 0
Simplifying the equation, we get:
3x + 6 = 0
Subtracting 6 from both sides, we get:
3x = -6
Dividing both sides by 3, we get:
x = -2
Now that we have the value of x, we can substitute it back into either equation to find the value of y. Let’s use the first equation:
y = x + 6
y = -2 + 6
y = 4
Therefore, the solution to the system of equations y=x+6 and y+2x=0 is (x, y) = (-2, 4).