Linear / Quadratic Systems of Equations

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What is a linear equation?

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What is a quadratic equation?

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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 lines represented by the equations are parallel and never intersect.

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What does it mean for a system of equations to have one solution?

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A system of equations has one solution when the lines represented by the equations intersect at exactly one point.

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

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A system of equations has two solutions when the graphs of the equations intersect at two distinct points.

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How do you solve a system of linear and quadratic equations graphically?

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To solve graphically, plot both equations on the same graph and identify the points where they intersect. These points are the solutions.

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How do you solve a system of linear and quadratic equations algebraically?

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To solve algebraically, substitute the linear equation into the quadratic equation and solve for the variable.

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What is the vertex of a parabola represented by a quadratic equation?

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What is the discriminant in a quadratic equation?

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What is the slope-intercept form of a linear equation?

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