To find the solution to the system of equations given by:
- \( y = 2x + 3 \)
- \( y = -3x + 3 \)
We can set the right sides of the equations equal to each other, since both expressions equal \( y \).
So we can write:
\[ 2x + 3 = -3x + 3 \]
Next, let's solve for \( x \):
- Add \( 3x \) to both sides:
\[ 2x + 3x + 3 = 3 \]
which simplifies to:
\[ 5x + 3 = 3 \]
- Subtract \( 3 \) from both sides:
\[ 5x = 0 \]
- Divide both sides by \( 5 \):
\[ x = 0 \]
Now that we have \( x = 0 \), we can substitute this value back into either equation to find \( y \). We'll use the first equation:
\[ y = 2(0) + 3 = 3 \]
So, the solution to the system of equations is:
\[ \begin{align*} x & = 0 \ y & = 3 \end{align*} \]
Thus, the solution is \( (x, y) = (0, 3) \).