For solving each pair of equations, in this exercise, use the method of elimination by equation coefficients :
y = 2x - 6
y = 0

Answer

To solve the given pair of equations using the method of elimination by equating coefficients, we have the following equations:

1. \( y = 2x - 6 \) (Equation 1)
2. \( y = 0 \) (Equation 2)

### Step 1: Rewrite the equations in standard form
We will first rewrite both equations in the standard form \( Ax + By = C \).

From Equation 1:
\[ y - 2x + 6 = 0 \]
This can be rearranged to:
\[ -2x + y = 6 \] (Equation 3)

From Equation 2:
\[ y = 0 \]
This can be rewritten as:
\[ 0x + y = 0 \] (Equation 4)

### Step 2: Align the equations for elimination
Now we have the equations in standard form:
1. \( -2x + y = 6 \) (Equation 3)
2. \( 0x + y = 0 \) (Equation 4)

### Step 3: Eliminate \( y \)
To eliminate \( y \), we can subtract Equation 4 from Equation 3:

\[ (-2x + y) - (0x + y) = 6 - 0 \]

This simplifies to:
\[ -2x = 6 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{6}{-2} = -3 \]

### Step 5: Substitute \( x \) back to find \( y \)
Now we substitute \( x = -3 \) back into either original equation to find \( y \). We can use Equation 2:
\[ y = 0 \]

### Final Solution
Thus, the solution to the system of equations is:
\[ x = -3, \quad y = 0 \]