SAT Math: Systems of Nonlinear Equations
23+ practice questions in Praczo
The concept, explained
- 1
A system of equations involving at least one non-linear equation (often a quadratic or a circle) can have 0, 1, 2, or more solutions.
- 2
Substitution is usually the best algebraic method: solve the linear equation for one variable and substitute it into the non-linear equation.
- 3
Graphically, the solutions correspond to the points where the shapes intersect (e.g., a line crossing a parabola).
- 4
If substituting produces a quadratic equation, use the discriminant (b² - 4ac) to find the number of intersections without fully solving it.
- 5
Watch out for extraneous solutions when squares/roots are involved.
- ✗ Forgetting that a line can intersect a parabola or circle at two points and thus expecting only one (x,y) pair.
- ✗ Failing to plug the x-values back into the linear equation to find the corresponding y-values.
SAT-style practice
How many intersection points exist between the line y = 3x + 1 and the parabola y = x² + 2x + 3?
Ready to master this concept?
Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required