Question

Find the solution to the system of equations.
{y=2x+3; y=-3x+3
x=
y=

Answer 1

To find the solution to the system of equations given by:

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

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 \( x \):

1. Add \( 3x \) to both sides:

\[
2x + 3x + 3 = 3
\]

which simplifies to:

\[
5x + 3 = 3
\]

2. Subtract \( 3 \) from both sides:

\[
5x = 0
\]

3. 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 \( (x, y) = (0, 3) \).