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Advanced PSAT Math: Nonlinear Systems and Exponential Models

Systems of Equations: Linear and Nonlinear

Advanced PSAT Math includes systems involving one linear and one quadratic equation. To solve: express the linear equation as y = mx + b, substitute into the quadratic, and solve the resulting quadratic. The discriminant of the resulting equation tells you how many intersection points exist: two intersections (discriminant > 0), one intersection (tangent, discriminant = 0), no real intersections (discriminant < 0). Example: y = 2x + 3 and y = x² − 2. Substitute: x² − 2 = 2x + 3 → x² − 2x − 5 = 0. Discriminant: 4 + 20 = 24 > 0, so two intersection points. PSAT questions may present the system in graphical form and ask for the number of solutions — recognize that a line tangent to a parabola means exactly one solution.

Advanced PSAT Math: Nonlinear Systems and Exponential Models

Systems of Equations: Linear and Nonlinear

Advanced PSAT Math includes systems involving one linear and one quadratic equation. To solve: express the linear equation as y = mx + b, substitute into the quadratic, and solve the resulting quadratic. The discriminant of the resulting equation tells you how many intersection points exist: two intersections (discriminant > 0), one intersection (tangent, discriminant = 0), no real intersections (discriminant < 0). Example: y = 2x + 3 and y = x² − 2. Substitute: x² − 2 = 2x + 3 → x² − 2x − 5 = 0. Discriminant: 4 + 20 = 24 > 0, so two intersection points. PSAT questions may present the system in graphical form and ask for the number of solutions — recognize that a line tangent to a parabola means exactly one solution.