Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables.

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

Back

It means that the equations represent parallel lines that never intersect.

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What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

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What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b.

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What is a quadratic equation?

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An equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants.

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How can you graph a system of equations?

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By plotting each equation on the same coordinate plane and identifying the intersection points.

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What is substitution in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is elimination in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What does it mean if a system of equations has infinitely many solutions?

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It means that the equations represent the same line, and every point on that line is a solution.

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What is the graphical representation of a quadratic function?

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A parabola, which can open upwards or downwards depending on the coefficient of x².