The example below will show you how to find solution(s) to a system of one linear and one non-linear equation using a table. The process is like using a table to find the solution for a system of linear equations except there may be more points of intersection.

Example: Solve the system Set of two equations: y=3x^2 + 8x+2; y=2(x+2) + 7 using a data table.

Solution: Enter both equations into your graphing calculator and get an idea about the points of intersection by taking a quick look at the graph. One of these equations is a parabola. Remember from the video, there could possibly be two points of intersection.

graphing calculator screen showing y1=3x2+8x+2 and y2=2(x+2)+7, graphing calculator screen showing graphs of y=3x2+8x+2 and y=2(x+2)+7

There, indeed, are two points of intersection. Set the table to start around x = -4.

graphing calculator screen showing a table of values for X,Y1,Y2 from x=-4 to x=2 with values at x = -3 and x=1 circled

Fortunately, this time, both points of intersection are found within this window. If they had not been, we would have needed to scroll through the table. The solutions are both (-3, 5) and (1, 13).

Try this problem on your own:

Solve:Set of two equations: x+y=7; x^2 + y=9

Interactive popup. Assistance may be required.

Check Your Answer

Solution:

x + y = 7 becomes y = 7 - x

x2 + y = 9 becomes y = 9 - x2

Graphing calculator screen shot equation input screen; table with x and y values

The solutions are (-1, 8) and (2, 5)Close Pop Up