Systems of Linear Equations - All Methods

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear 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 to solve a system of equations using elimination?

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Elimination is a method for solving a system of equations by adding or subtracting the equations to eliminate one variable, making it easier to solve for the other variable.

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What is the graphical representation of a linear equation?

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A linear equation can be represented graphically as a straight line on a coordinate plane, where the x-axis represents the independent variable and the y-axis represents the dependent variable.

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

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How do you find the intersection point of two lines?

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What is the substitution method in 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 to solve for the second variable.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system of equations.

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What does it mean if two lines are coincident in a system of equations?

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If two lines are coincident, they lie on top of each other, meaning they have the same slope and y-intercept, resulting in infinitely many solutions.

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How can you represent a real-world situation as a system of equations?

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To represent a real-world situation as a system of equations, identify the variables, write equations based on the relationships between the variables, and ensure they reflect the constraints of the situation.

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What is the purpose of graphing a system of equations?

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Graphing a system of equations visually shows the relationship between the equations and helps identify the solution(s) by finding the intersection points.