Alg/Geo III - 4.8 Solving Nonlinear System of Equations

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Solve the system by graphing:

$$y=x^2+4x-4\ and\ y=2x-5$$

Where do these graphs intersect?

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Solve the system by graphing:

$$y=-x+6\ and\ y=-2x^2-x+3$$

Where do these graphs intersect?

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Solve the system by graphing:

$$y=3x-15\ and\ y=\frac{1}{2}x^2-2x-7$$

Where do these graphs intersect?

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Solve the system by substitution:

$$y=-5x\ and\ y=x^2-3x-3$$

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Solve the system by elimination:

$$y=5x-4\ and\ y=9x^2+8x-6$$

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Multiple Choice

Which method can be used to find the exact solution for the system of equations below?

$$y=x^2-4x+3\ and\ y=x-1$$

• Graphing

• Substitution

• Elimination

• All of the above

Multiple Choice

When solving a nonlinear system of equations by graphing, what does it mean if the graphs do not intersect?

• The system has one solution.

• The system has two solutions.

• The system has an infinite number of solutions.

• The system has no solution.

Multiple Choice

If the quadratic equation of a nonlinear system has no real solutions, what does this mean for the system of equations?

• The system has one real solution.

• The system has two real solutions.

• The system has multiple real solutions.

• The system has no real solutions.

Open Ended

Approximate the solutions of the system to the nearest thousandth.

$$y=4^x\ and\ y=x^2+x+3$$