Question

How many solutions does the system of equations have? 6x+2y=−18 3x+y=24

Answer 1

To determine the number of solutions for the system of equations, we can either solve them or analyze their relationship. Let’s first write down the equations:

1. \( 6x + 2y = -18 \)
2. \( 3x + y = 24 \)

Let's simplify the first equation by dividing everything by 2:

\[
3x + y = -9
\]

Now we have the following system of equations:

1. \( 3x + y = -9 \)
2. \( 3x + y = 24 \)

Next, we can see that both equations have the same left-hand side (the expressions \(3x + y\)), but they have different right-hand sides.

This indicates that the two lines represented by these equations are parallel and will never intersect. Since they do not intersect, there is no solution to the system of equations.

Thus, the system of equations has **0 solutions**.