Final answer:
The lines represented by the equations 3y + 2x = -24 and y = (2/3)x - 6 intersect at the point (-3, -12).
Step-by-step explanation:
The lines represented by the equations 3y + 2x = -24 and y = (2/3)x - 6 are:
-24 - 2x = 3y
y = (2/3)x - 6
By substituting the value of y from the second equation into the first equation:
-24 - 2x = 3((2/3)x - 6)
Simplifying the equation:
-24 - 2x = 2x - 18
Combining like terms:
-4x = 6
Dividing both sides by -4:
x = -6/2 = -3
Substituting the value of x into the second equation:
y = (2/3)(-3) - 6 = -6 - 6 = -12
Therefore, the lines represented by the equations 3y + 2x = -24 and y = (2/3)x - 6 intersect at the point (-3, -12).