1600SAT Logo All SAT Skills
    Advanced MathHard

    Nonlinear equations in one variable and systems of equations

    Solve quadratic and other nonlinear equations using factoring, the quadratic formula, and substitution into systems.

    Sample SAT Problem

    Solve x² − 5x + 6 = 0.

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    Step-by-Step Solution

    Factor: (x − 2)(x − 3) = 0. Solutions: x = 2 or x = 3.

    Key Tips from Pamela

    • The quadratic formula works for any quadratic, even when factoring is hard.
    • The discriminant (b² − 4ac) tells you the number of real solutions.
    • When substituting into a system, watch for extraneous solutions.

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