To solve the system of equations given by:
- \( y = 4x - 9 \)
- \( -7x - 6y = -39 \)
we can use substitution, as we already have \( y \) expressed in terms of \( x \) from the first equation.
Step 1: Substitute \( y \) in the second equation
Substituting \( y = 4x - 9 \) into the second equation:
\[ -7x - 6(4x - 9) = -39 \]
Step 2: Simplify the equation
Distributing the \(-6\):
\[ -7x - 24x + 54 = -39 \]
Combine like terms:
\[ -31x + 54 = -39 \]
Step 3: Solve for \( x \)
Now, we isolate \( x \):
\[ -31x = -39 - 54 \] \[ -31x = -93 \]
Dividing both sides by \(-31\):
\[ x = \frac{-93}{-31} = 3 \]
Step 4: Substitute \( x \) back to find \( y \)
Now we substitute \( x = 3 \) back into the first equation to find \( y \):
\[ y = 4(3) - 9 \] \[ y = 12 - 9 = 3 \]
Solution
The solution to the system of equations is:
\[ x = 3, \quad y = 3 \]
You can express this as the coordinate point \((3, 3)\).