2.5.2

Simultaneous Equations Graphs

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Solving Nonlinear Systems of Equations

A system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear.

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Linear and parabola

  • There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.
  • The points where the lines cross are solutions to both equations.
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Linear and parabola

  • In the image, the functions y=x2+1y = x^2 + 1 and xy=1x-y=-1 are plotted.
  • The points of intersection are (0,1)(0,1) and (1,2)(1,2), so the solutions of this system of equations are:
    • x=0,y=1x=0, y=1 and x=1,y=2x=1,y=2
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Linear and circle

  • Just as with a parabola and a line, there are three possible outcomes when solving a system of equations representing a circle and a line.
  • The line that has one solution is tangent to the circle and intersects the circle at exactly one point.
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Linear and circle

  • In the image, the functions x2+y2=5x^2+y^2 = 5 and y=3x5y=3x-5 are plotted.
  • The points of intersection are (2,1)(2,1) and (1,2)(1,-2), so the solutions of this system of equations are:
    • x=2,y=1x=2, y=1 and x=1,y=2x=1,y=-2

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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