Question

The system of equations y = negative 3 x + 2 and y = one-half x minus 6 is shown on the graph below.

On a coordinate plane, 2 lines intersect around (2.3, negative 4.75).

What is a reasonable estimate for the solution?
(2 and one-third, negative 4 and three-fourths)
(negative 4 and three-fourths, 2 and one-third)
(2 and two-thirds, negative 4 and one-half)
(Negative 4 and one-half, 2 and two-thirds)

Answer 1

To determine a reasonable estimate for the solution of the system of equations given the intersection point of the two lines, let's interpret the approximate coordinates (2.3, -4.75) provided.

**Approximate solution:** The coordinates suggest that the x-coordinate is approximately 2.3 and the y-coordinate is approximately -4.75.

Now, let's compare this with the provided options:

1. **(2 and one-third, negative 4 and three-fourths)** - This is approximately (2.333, -4.75).
2. **(negative 4 and three-fourths, 2 and one-third)** - This is ( -4.75, 2.333).
3. **(2 and two-thirds, negative 4 and one-half)** - (2.667, -4.5).
4. **(Negative 4 and one-half, 2 and two-thirds)** - (-4.5, 2.667).

Among these options, the first option **(2 and one-third, negative 4 and three-fourths)**, which is approximately (2.333, -4.75), is the closest to the estimated coordinates (2.3, -4.75) that you provided.

Therefore, the most reasonable estimate for the solution is:

**(2 and one-third, negative 4 and three-fourths)**