Question

On a coordinate plane, a line goes through (0, 4) and (4, 16).
The line representing the first table is shown in the graph. What is the solution to the system of linear equations represented by both tables?

2 tables. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries negative 2, 4, 10, 16. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries 18, 16, 14, 12.

Answer 1

To find the solution to the system of linear equations represented by both tables, we first identify the equations of the lines corresponding to the two tables.

### First Table
**Entries:**
- (-2, -2)
- (0, 4)
- (2, 10)
- (4, 16)

To find the equation of the line, we will use two points from the table. Let's use (0, 4) and (4, 16).

The slope (m) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{16 - 4}{4 - 0} = \frac{12}{4} = 3
\]

Now we can use the point-slope form of the line \(y - y_1 = m(x - x_1)\). Taking point (0, 4):

\[
y - 4 = 3(x - 0)
\]
\[
y = 3x + 4
\]

### Second Table
**Entries:**
- (-2, 18)
- (0, 16)
- (2, 14)
- (4, 12)

Again, we can choose two points. Let's take (0, 16) and (4, 12) for calculating the equation.

The slope (m) is:

\[
m = \frac{12 - 16}{4 - 0} = \frac{-4}{4} = -1
\]

Using the point-slope form with point (0, 16):

\[
y - 16 = -1(x - 0)
\]
\[
y = -x + 16
\]

### Setting the Equations Equal
Now we set the two equations equal to find the intersection point:

\[
3x + 4 = -x + 16
\]

Solving for \(x\):

\[
3x + x = 16 - 4
\]
\[
4x = 12
\]
\[
x = 3
\]

### Finding the Corresponding \(y\)
Now we can substitute \(x = 3\) back into either equation to find \(y\). We'll use \(y = 3x + 4\):

\[
y = 3(3) + 4 = 9 + 4 = 13
\]

### Conclusion
Thus, the solution to the system of equations represented by both tables is:

\[
\boxed{(3, 13)}
\]