Question

Solve the system of equations. {y=−2x+13y−9=6x

Answer 1

To solve the system of equations given by:

1. \( y = -2x + 13 \)
2. \( y - 9 = 6x \)

we can start by rewriting the second equation in a more manageable form.

From equation 2, rearranging gives:

\[
y = 6x + 9
\]

Now we have the system:

1. \( y = -2x + 13 \)
2. \( y = 6x + 9 \)

Next, we can set the two expressions for \( y \) equal to each other:

\[
-2x + 13 = 6x + 9
\]

Now, we can solve for \( x \).

First, add \( 2x \) to both sides:

\[
13 = 8x + 9
\]

Next, subtract \( 9 \) from both sides:

\[
4 = 8x
\]

Now, divide both sides by \( 8 \):

\[
x = \frac{4}{8} = \frac{1}{2}
\]

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

\[
y = -2\left(\frac{1}{2}\right) + 13
\]

Calculating this gives:

\[
y = -1 + 13 = 12
\]

Thus, the solution to the system of equations is:

\[
(x, y) = \left(\frac{1}{2}, 12\right)
\]