How many solutions does the system of equations have?
6x + 2 y =-18
3x + y = 24
This system of equations has only one solution.
To determine the number of solutions for a system of equations, we can solve the equations and see if there is a unique solution, infinitely many solutions, or no solution.
Let's solve the given system of equations using the method of substitution:
First, rearrange the second equation to solve for y:
y = 24 - 3x
Now substitute this expression for y in the first equation:
6x + 2(24 - 3x) = -18
Simplify the equation:
6x + 48 - 6x = -18
Combine like terms:
48 = -18
Since this equation is false, there is no solution to the system of equations.
Therefore, the system of equations has no solution.