Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
4x + 4y = -36
4x + 4y = 12
They have the same slope !
Those are two parallel lines which never cross. There is no solution.
To solve the given system of equations using the substitution method, we need to rearrange one of the equations to isolate one of the variables, and then substitute that expression into the other equation.
Let's rearrange the first equation to solve for x:
4x + 4y = -36
Subtract 4y from both sides:
4x = -36 - 4y
Divide both sides by 4:
x = (-36 - 4y) / 4
Simplify:
x = -9 - y
Now we can substitute this expression for x into the second equation:
4x + 4y = 12
Replace x with -9 - y:
4(-9 - y) + 4y = 12
Distribute:
-36 - 4y + 4y = 12
Combine like terms:
-36 = 12
Since the equation -36 = 12 is not true, the system of equations has no solution.