How many solutions does the system of equations have?
y equals negative 2 x plus 9 line break 6 x plus 3 y equals 27
To find the number of solutions for the system of equations, we can solve the system using any method. Let's start by solving the system using the substitution method.
First, we'll solve the first equation for y:
y = -2x + 9
Now, substitute this value of y into the second equation:
6x + 3(-2x + 9) = 27
6x - 6x + 27 = 27
27 = 27
As we can see, the equation obtained is true, which means that every value of x satisfies the equation. Therefore, the system of equations has infinitely many solutions.