x – 4y = 12 and 5x – 20y = 60
To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the substitution method.
From the first equation, we can solve for x in terms of y:
x = 12 + 4y
Now, substitute this expression for x in the second equation:
5(12 + 4y) - 20y = 60
Distribute the 5:
60 + 20y - 20y = 60
Combine like terms:
60 = 60
This equation is always true, which means that the system of equations has infinitely many solutions. This is because the two equations are essentially the same equation, just written in different form.