CPA2 - 3.5 Flashcard Solving Nonlinear Systems of Equations

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What is a nonlinear system of equations?

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A nonlinear system of equations is a set of equations in which at least one of the equations is not linear, meaning it cannot be represented as a straight line on a graph.

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What does it mean to find the solution of a system of equations?

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Finding the solution of a system of equations means determining the values of the variables that satisfy all equations in the system simultaneously.

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What is the graphical method for solving systems of equations?

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The graphical method involves plotting each equation on a graph and identifying the point(s) where the graphs intersect, which represent the solutions.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is a linear equation?

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A linear equation is an equation that can be written in the form ax + by = c, where a, b, and c are constants and x and y are variables.

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What is a quadratic equation?

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A quadratic equation is an equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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A system of equations has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

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How do you determine the number of solutions in a system of equations graphically?

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You determine the number of solutions by analyzing the intersection points of the graphs: one intersection point indicates one solution, no intersection points indicate no solution, and overlapping lines indicate infinitely many solutions.