System of Equations Flashcard Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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

Back

A system 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 has one solution when the lines intersect at exactly one point.

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

Back

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

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How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

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

Back

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How do you find the solution to a system of equations graphically?

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To find the solution graphically, plot both equations on the same graph and identify the point(s) where they intersect.

Front

What is the significance of the y-intercept in a linear equation?

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Front

What is the method of substitution in solving systems of equations?

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

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What is the method of elimination in solving systems of equations?

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