Graphs can be used to solve systems of equations. This method, however, usually allows only approximate solutions, whereas the algebraic method arrives at exact solutions.
Example 1: Solve the following system of equations graphically.
Equation (1) is the equation of an ellipse. Convert the equation into standard form.
The major intercepts are at
and
, and the minor intercepts are at
and
.
Equation (2) is the equation of a hyperbola. Convert the equation into standard form.
The transverse axis is horizontal and the vertices are at
and
, as shown in Figure
1 .
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Figure 1
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Approximate solutions to hyperbola and ellipse.
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The approximate answers are
The exact answers are
Example 2: Solve the following system of equations graphically.
Equation (1) is the equation of a circle centered at (0, 0) with a radius of 10. Equation (2) is the equation of a line. The solutions are
The graph is shown in Figure
2 .
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Figure 2
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Circle with intersecting line.
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Linear Sentences in One Variable
Quadratic Systems
