Systems of equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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

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It means that there is no set of values for the variables that can satisfy all equations in the system, often because the lines are parallel.

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

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It means that there are an infinite number of solutions, typically because the equations represent the same line.

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How do you solve a system of equations using 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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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines of the equations plotted on a coordinate plane, where the intersection point(s) represent the solution(s).

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

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How can you determine if a system of equations has no solution graphically?

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If the lines representing the equations are parallel, they will never intersect, indicating no solution.

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How can you determine if a system of equations has infinite solutions graphically?

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If the lines representing the equations overlap completely, they represent the same line, indicating infinite solutions.