🍁 FLASHCARD - Solving Systems of Equations

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What is a system of equations?

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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 on a graph.

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What does it mean if a system of equations has a unique solution?

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It means that the graphs of the equations intersect at exactly one point, indicating one set of values for the variables.

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What does it mean if a system of equations has no solution?

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It means that the graphs of the equations are parallel and never intersect, indicating that there are no values for the variables that satisfy both equations.

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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, so every point on the line is a solution.

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

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

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What is the elimination method for 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 other variable.

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What is the substitution method for 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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How do you graph a system of equations?

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To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where they intersect.

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

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What is the standard form of a linear equation?

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