how many solutions does the system of equations have?
3x=-12y+15
x+4y=5
To find how many solutions the system of equations has, we can solve the equations using any method and see if the solutions exist or not.
Let's solve the given system of equations using the substitution method:
First, let's solve the first equation for x:
3x = -12y + 15
Divide both sides by 3:
x = -4y + 5
Now, substitute this expression for x in the second equation:
x + 4y = 5
(-4y + 5) + 4y = 5
-4y + 5 + 4y = 5
Combine like terms:
5 = 5
The equation simplifies to 5 = 5, which is a true statement.
Since the equation is true, it means that the two original equations represent the same line and the system has infinitely many solutions.
In conclusion, the given system of equations has infinitely many solutions.