Question

Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer.

y = 12
x + 2
2y = x + 4

The system of equations has
Choose...
. The two equations represent
Choose...
.

Answer 1

To solve the system of equations using substitution, let's first clarify the two equations given:

1. \( y = 12 \)
2. \( 2y = x + 4 \)

### Step 1: Substitute the value of \( y \)
Since the first equation directly states that \( y = 12 \), we can substitute this value into the second equation.

### Step 2: Substitute and solve the second equation
Substituting \( y = 12 \) into the second equation:
\[
2(12) = x + 4
\]
\[
24 = x + 4
\]
Now, solve for \( x \):
\[
x = 24 - 4
\]
\[
x = 20
\]

### Solution
The solution to the system of equations is \( x = 20 \) and \( y = 12 \).

### Answer to the drop-down menus:
**The system of equations has**: one unique solution.
**The two equations represent**: a point of intersection on the coordinate plane.

So, the final answer is:
1. The system of equations has **one unique solution**.
2. The two equations represent **a point of intersection on the coordinate plane**.