Nonlinear equations in one variable and systems of equations in two variables: practice and worksheets
Solve quadratic and other nonlinear equations, and find intersections in linear–nonlinear systems.
Concept overview
Nonlinear equations may have several real solutions because a curved graph can cross a line or the x-axis more than once. Factoring, square roots, substitution, and graph interpretation are common methods.
Key points
- Move all terms to one side before factoring a quadratic equation.
- Check for extraneous solutions after squaring or other non-reversible steps.
- In a system, each intersection point is a solution to both equations.
Worked example
Solving x² − 5x + 6 = 0 gives (x − 2)(x − 3) = 0, so the solutions are x = 2 and x = 3.
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Questions by difficulty
Nonlinear equations in one variable and systems of equations in two variables worksheet practice
Use the printable worksheet for independent practice, then check the answer key and worked explanations.
Frequently asked questions
How should I practice Nonlinear equations in one variable and systems of equations in two variables?
Start with foundation questions, check each answer, and move up a level after several correct answers in a row.
How many practice questions are available?
IQClub currently has 273 published questions for this skill.
Can I use this for test preparation?
Yes. The practice reinforces school mathematics and the same reasoning used in high-school tests and entrance exams.