How many solutions does the system of equations have?
3x = -12y + 15 and x + 4y = 5
To determine the number of solutions, we can solve the system of equations using any method, such as substitution or elimination.
We will use the elimination method:
Multiply the second equation by 3 to make the coefficients of x in both equations equal:
3(x + 4y) = 3(5)
3x + 12y = 15 (multiplied both sides of the equation by 3)
Now the two equations are:
3x = -12y + 15
3x + 12y = 15
Adding these two equations eliminates the variable y:
3x + 3x + 12y + (-12y) = 15 + 15
6x = 30
x = 30/6
x = 5
Substitute this value of x into one of the original equations:
x + 4y = 5
5 + 4y = 5
4y = 0
y = 0/4
y = 0
So the system of equations has a unique solution: x = 5, y = 0.
Therefore, the system of equations has 1 solution.