Question
-3x + 2y = -6
9x - 6y = 9
9x - 6y = 9
Answers
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Answered by
GPT-4o mini
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.
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.
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