Question

The linear equation y = negative 2 x + 4 is represented on the graph below.


On a coordinate plane, a line goes through (0, 4) and (2, 0).


A second linear equation is represented by the data in the table.

x
y
–4
–3
0
–1
2
0
6
2

What is the solution to the system of equations?
(2, 0)
(0, 4)
(0, –1)
(4, –4)

Answer 1

To find the solution to the system of equations, we need to identify where the line represented by the equation \( y = -2x + 4 \) intersects with the line or points represented by the data in the table.

First, we check the equation of the first line:

The equation is \( y = -2x + 4 \). We can find points on this line by plugging in values for \( x \):

- For \( x = 0 \):
\( y = -2(0) + 4 = 4 \) → Point (0, 4)

- For \( x = 2 \):
\( y = -2(2) + 4 = 0 \) → Point (2, 0)

Now, we have points (0, 4) and (2, 0) on the line given by the equation.

Next, let's examine the points given in the table:

| x | y |
|----|-----|
| -4 | 6 |
| -3 | 2 |
| 0 | -1 |
| -1 | 0 |
| 2 | 0 |
| 0 | 6 |

From this table, we note the following points:
- (0, -1)
- (2, 0)

Next, we check if these points satisfy the equation \( y = -2x + 4 \):

1. For \( (0, -1) \):
- Substitute \( x = 0 \):
\( y = -2(0) + 4 = 4 \) (not equal to -1)

2. For \( (2, 0) \):
- Substitute \( x = 2 \):
\( y = -2(2) + 4 = 0 \) (which is equal to 0)

The point (2, 0) is indeed on both the line represented by the equation and in the data table.

Now, looking at the answer choices provided:

- (2, 0)
- (0, 4)
- (0, -1)
- (4, -4)

The solution to the system of equations is \( \boxed{(2, 0)} \).