Systems of Linear Equations

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What is a system of linear equations?

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

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

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The lines intersect at exactly one point, representing a unique solution for the variables.

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

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The lines are parallel and never intersect, indicating that there is no set of values for the variables that satisfies both equations.

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

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The lines coincide, meaning they are the same line, and there are countless points that satisfy both equations.

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How can you determine the number of solutions in a system of equations by graphing?

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By plotting the equations on a graph and observing the intersection points.

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What is the substitution method 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 the elimination method 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 is the graphical representation of a linear equation?

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A straight line on a coordinate plane, where each point on the line represents a solution to the equation.

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

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How do you find the slope of a line given two points?

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