To find the solution of the system of equations given by:
- \(-3x - y = 3\)
- \(y = -3x + 4\)
we can use the substitution method, as the second equation is already solved for \(y\). We can substitute \(y\) from the second equation into the first equation.
Starting with the first equation:
\(-3x - y = 3 \)
Substituting \(y = -3x + 4\):
\[ -3x - (-3x + 4) = 3 \]
This simplifies to:
\[ -3x + 3x - 4 = 3 \]
The \(-3x\) and \(3x\) cancel each other out:
\[ -4 = 3 \]
This statement is false, which means that the two lines represented by the equations do not intersect. Therefore, there is no solution to the system of equations; in other words, the lines are parallel.
In conclusion, the system has no solution.
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