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-3x + 2y = -6

9x - 6y = 9

1 answer

To solve the system of equations:

  1. \(-3x + 2y = -6\) (Equation 1)
  2. \(9x - 6y = 9\) (Equation 2)

Let's simplify Equation 2 first. Notice that we can divide all terms by 3:

\[ 3x - 2y = 3 \quad \text{(Equation 2 simplified)} \]

Now we have:

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

Next, we can add both equations together to eliminate \(y\):

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

This simplifies to:

\[ 0 = -3 \]

Since this statement is false (0 does not equal -3), it indicates that the equations are inconsistent and, therefore, there is no solution to the system of equations. The lines represented by these equations are parallel and do not intersect.