To solve the system of equations using substitution, we have the equations:
- \( 5x - 2y = -6 \)
- \( y = 3x + 3 \)
We can substitute the expression for \(y\) from the second equation into the first equation.
Substituting \(y = 3x + 3\) into the first equation:
\[ 5x - 2(3x + 3) = -6 \]
Now, simplify this equation:
\[ 5x - 6x - 6 = -6 \]
Combine like terms:
\[ -1x - 6 = -6 \]
Adding 6 to both sides gives:
\[ -1x = 0 \]
Thus:
\[ x = 0 \]
Now that we have \(x\), we can find \(y\) by substituting \(x = 0\) back into the second equation:
\[ y = 3(0) + 3 = 3 \]
So we have the solution:
\[ (x, y) = (0, 3) \]
The answer is \((0, 3)\).