Question

Solving Equations Using Substitution Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
How many solutions does the system of equations have?
6x+2y=−18

3x+y=24

Answer 1

To determine how many solutions the system of equations has, we can solve the equations using substitution or elimination. Let's start by rewriting both equations:

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

**Step 1**: Solve Equation 2 for \( y \).

From Equation 2:
\[
y = 24 - 3x \tag{Equation 3}
\]

**Step 2**: Substitute Equation 3 into Equation 1.

Substituting \( y \) from Equation 3 into Equation 1:
\[
6x + 2(24 - 3x) = -18
\]
\[
6x + 48 - 6x = -18
\]
\[
48 = -18
\]

Since \( 48 \neq -18\), we have found a contradiction.

This means that the system of equations is inconsistent and thus there are **no solutions** to the system.

**Conclusion**: The system of equations has no solutions.