Question

Solve each system. Answer should be an ordered pair (x, y)
-
1) y = 12x + 13
y = 9x + 10

Answer 1

To solve the system of equations:

1) \( y = 12x + 13 \)

2) \( y = 9x + 10 \)

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

\[ 12x + 13 = 9x + 10 \]

Now, subtract \( 9x \) from both sides:

\[ 12x - 9x + 13 = 10 \]

This simplifies to:

\[ 3x + 13 = 10 \]

Next, subtract 13 from both sides:

\[ 3x = 10 - 13 \]

This simplifies to:

\[ 3x = -3 \]

Now, divide both sides by 3 to solve for \( x \):

\[ x = -1 \]

Now that we have \( x \), we can substitute it back into either of the original equations to solve for \( y \). We'll use the second equation:

\[ y = 9(-1) + 10 \]

This simplifies to:

\[ y = -9 + 10 \]

So:

\[ y = 1 \]

Thus, the solution to the system of equations is the ordered pair:

\[
\boxed{(-1, 1)}
\]