y = –6x + 3

y = –9x + 9

1 answer

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:

\[ 3x + 3 = 9 \]

  1. Subtract 3 from both sides:

\[ 3x = 6 \]

  1. 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:

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