Question

x values y = 6x - 1 y = 3x + 2
-1
0
1
2
3
The ordered pair that is a solution to the system of equations is

Answer 1

To find the ordered pairs that are solutions to the system of equations given by \( y = 6x - 1 \) and \( y = 3x + 2 \), we will first calculate the \( y \) values for each \( x \) in the table for both equations, then we can look for points where both equations give the same \( y \) value.

Given the \( x \) values: -1, 0, 1, 2, 3, we will compute:

**For \( y = 6x - 1 \):**
- For \( x = -1 \): \( y = 6(-1) - 1 = -6 - 1 = -7 \)
- For \( x = 0 \): \( y = 6(0) - 1 = 0 - 1 = -1 \)
- For \( x = 1 \): \( y = 6(1) - 1 = 6 - 1 = 5 \)
- For \( x = 2 \): \( y = 6(2) - 1 = 12 - 1 = 11 \)
- For \( x = 3 \): \( y = 6(3) - 1 = 18 - 1 = 17 \)

**For \( y = 3x + 2 \):**
- For \( x = -1 \): \( y = 3(-1) + 2 = -3 + 2 = -1 \)
- For \( x = 0 \): \( y = 3(0) + 2 = 0 + 2 = 2 \)
- For \( x = 1 \): \( y = 3(1) + 2 = 3 + 2 = 5 \)
- For \( x = 2 \): \( y = 3(2) + 2 = 6 + 2 = 8 \)
- For \( x = 3 \): \( y = 3(3) + 2 = 9 + 2 = 11 \)

Now we compile the results:

\[
\begin{array}{|c|c|c|}
\hline
x & y = 6x - 1 & y = 3x + 2 \\
\hline
-1 & -7 & -1 \\
0 & -1 & 2 \\
1 & 5 & 5 \\
2 & 11 & 8 \\
3 & 17 & 11 \\
\hline
\end{array}
\]

Next, let's look for the \( (x, y) \) pairs where the two equations yield the same \( y \):

- For \( x = 1 \): Both equations yield \( y = 5 \).
- For \( x = 3 \): The first equation gives \( y = 17 \) and the second gives \( y = 11 \) (not a match).

Thus, the only solution to the system of equations is:

\[
\boxed{(1, 5)}
\]