Question

y = –6x + 3
y = –9x + 9

Answer 1

To solve the system of equations given by:

1. \( y = -6x + 3 \)
2. \( y = -9x + 9 \)

we can set the two equations equal to each other since they both equal \( y \):

\[
-6x + 3 = -9x + 9
\]

Next, we will solve for \( x \):

1. Add \( 9x \) to both sides:

\[
-6x + 9x + 3 = 9
\]

This simplifies to:

\[
3x + 3 = 9
\]

2. Subtract 3 from both sides:

\[
3x = 6
\]

3. Divide by 3:

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into either equation to find \( y \). We will use the first equation:

\[
y = -6(2) + 3
\]

Calculating this gives:

\[
y = -12 + 3 = -9
\]

Thus, the solution to the system of equations is:

\[
\boxed{(2, -9)}
\]