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Solving A System Of Equations By Graphing

by e-Tutor

In this lesson you will be exploring mathematics by using a fun, interesting and investigative tool, the e-Tutor Graphic Calculator.
Are you ready?

Lesson Problem

How would you solve a system of equations using the e-Tutor Graphing Calculator?


Study Guide

Solving a Linear-Quadratic System by Graphing involves graphing each equation on the same set of axes and locating points of intersection, if any.

For the purpose of this lesson, one equation will be linear, which will be a straight line in the form of:
y = mx + b when graphed. The other equation will be a quadratic which will be a parabola in the form of:
y = ax2 + bx + c when graphed.

The solution set of a linear-quadratic system of equations, consists of:
a) two ordered pairs of numbers such as (x1,y1)(x2,y2)
b) one ordered pair of numbers such as (x,y)
c)no ordered pair which would be no solution.

Let's go through some examples.

Example 1:
a) Draw a graph of: y = -x2 + 4x - 3 for all values of x.
b) On the same set of axes, draw a graph of y = -x + 1.
c) Determine the solution set of the graphs drawn in part a and part b.

Note: The parabola opens downward because the x2 was a -x2.
Also, (2,1) is the turning point of the parabola.


Use the e-Tutor Graphing Calculator to graph the following linear-quadratic system of equations. For each system identify the solutions, y-intercepts and turning point of each parabola.

2x + y = 3
x 3y = 12

x + 3y = 3
-x + y = -3

5x +7y = -25
11x + 6y = -8

-3x +4y = 12
6x 8y =16

12x + 10y = -14
4x 3y = -11

Extended Learning

Use the e-Tutor Graphing Calculator to solve the following system of equations. Next, trace the graphs and mark the solutions.