How many solutions does the system of equations have?
x – 4y = 12 and y = x – 3
(1 point)
one
two
infinitely many
none
one
To determine the number of solutions, let's substitute the value of y from the second equation into the first equation:
x - 4(x - 3) = 12
Simplifying this equation, we get:
x - 4x + 12 = 12
-3x + 12 = 12
Subtracting 12 from both sides, we have:
-3x = 0
Dividing both sides by -3, we find:
x = 0
Now, substitute this value of x into the second equation:
y = 0 - 3
y = -3
So, the solution to the system of equations is x = 0 and y = -3.
Therefore, there is only one solution.
The answer is: one.