Solve using substitution.

y = –6x + 9
y = –4x + 5

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1 answer

To solve the system of equations using substitution, we first have the following two equations:

  1. \( y = -6x + 9 \)
  2. \( y = -4x + 5 \)

Since both equations are equal to \( y \), we can set them equal to each other:

\[ -6x + 9 = -4x + 5 \]

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

  1. Move \( -4x \) to the left side:

\[ -6x + 4x + 9 = 5 \]

This simplifies to:

\[ -2x + 9 = 5 \]

  1. Now, subtract 9 from both sides:

\[ -2x = 5 - 9 \]

\[ -2x = -4 \]

  1. Divide by -2:

\[ x = \frac{-4}{-2} = 2 \]

Now that we have the value of \( x \), we substitute it back into one of the original equations to find \( y \). We'll use the first equation:

\[ y = -6(2) + 9 \]

Calculating this gives:

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

Thus, the solution to the system of equations is:

\[ (x, y) = (2, -3) \]

So, the final answer is:

\[ \boxed{(2, -3)} \]