How do I solve the system of equations graphically, accurate to the nearest thousandth

(x^2/2) + (y^2/5) = 1

y=(1/3)x

To be able to graph accurately to a thousandth of a unit would obviously require a graphing calculator or computer which allows to to "zoom" in on the intersection.

Since we do not know what type of equipment you are using, we really cannot help you with the actual steps.
Your manual should describe that.

Your equations are
1. an ellipse with centre at the origin and
2. a straight line passing through the origin.

clearly there would be two solutions.

i have a graphing calculator TI-83 Plus

Do you use that calculator?

Yeah, i have that calculator too

To solve the system of equations graphically, accurate to the nearest thousandth, follow these steps:

1. Start by graphing the first equation, which is an ellipse. Note that the equation is in standard form, where (h, k) represents the center of the ellipse, and the denominators of x^2 and y^2 give you the lengths of the major and minor axes.
- First, find the center of the ellipse by setting x^2/2 and y^2/5 equal to zero. This gives you h = 0 and k = 0. So, the center of the ellipse is at the origin (0, 0).
- The major axis length is the square root of the denominator of x^2, which is sqrt(2). The minor axis length is the square root of the denominator of y^2, which is sqrt(5).
- Plot the center (0, 0), and then plot the points at (±sqrt(2), 0) and (0, ±sqrt(5)).
- Sketch an ellipse through these plotted points.
- Label this graph as Equation 1.

2. Next, graph the second equation, which represents a straight line. Since it is in slope-intercept form, y = mx + b, with m being the slope and b being the y-intercept, you can easily graph it.
- The slope, m, is 1/3, which means for every increase of 1 in x, y increases by 1/3.
- Plot the y-intercept, which is (0, 0). From there, move 1 unit to the right and 1/3 unit up, and plot another point.
- Sketch a line through these two points.
- Label this graph as Equation 2.

3. Analyze the graphs to find their points of intersection. These points will be the solutions to the system of equations.
- Look for the points where the ellipse and the line intersect on the graph.
- Estimate the coordinates of these points as accurately as possible.
- You can use the gridlines on the graph or a ruler to estimate the coordinates.
- Note down the estimated coordinates.
- Label these points as (x1, y1) and (x2, y2).

4. When you have the estimated coordinates, round them to the nearest thousandth to get the final answer.

So, to solve the system of equations graphically and accurately to the nearest thousandth, follow the steps outlined above.