Question

Solving Equations Using Substitution Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items








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

3x+y=24
(1 point)

Answer 1

To determine how many solutions the system of equations has, we can solve them using substitution or elimination.

First, let's rewrite the system of equations:

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

We can start by solving the second equation for \( y \):

From equation 2:
\[
y = 24 - 3x
\]

Now we can substitute this expression for \( y \) into the first equation:

\[
6x + 2(24 - 3x) = -18
\]

Now, distribute the 2:
\[
6x + 48 - 6x = -18
\]

Notice that \( 6x \) and \( -6x \) cancel each other out, leaving:
\[
48 = -18
\]

This statement is false, which means there are no values of \( x \) and \( y \) that satisfy both equations simultaneously.

Therefore, the system of equations has **no solutions**.

In summary, the system is inconsistent.