Alg II - Systems of Equations Flashcard

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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.

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What are the three methods to solve a system of equations?

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1. Graphing 2. Substitution 3. Elimination

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How do you solve a system of equations by substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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

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It means the lines represented by the equations are parallel and never intersect.

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

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It means the equations represent the same line, so 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?

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By analyzing the slopes and intercepts of the lines: - If slopes are equal and intercepts are different: No solution. - If slopes are equal and intercepts are the same: Infinitely many solutions. - If slopes are different: One solution.

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What is the elimination method?

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

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What is the graphical interpretation of a system of equations?

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The solution to a system of equations is the point(s) where the graphs of the equations intersect.

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How do you graph a linear equation?

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1. Find the y-intercept (where x=0). 2. Use the slope to find another point. 3. Draw the line through the points.

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

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