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.

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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the lines represented by the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the lines represented by the equations are parallel and never intersect.

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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.

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What is the elimination method in 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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How can you determine if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values of the variables back into the original equations. If both equations are true, the solution is correct.

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What is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the lines intersect.

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What is the point of intersection in a system of equations?

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The point of intersection is the solution to the system of equations, representing the values of the variables that satisfy all equations in the system.

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What does it mean for two lines to be parallel in the context of systems of equations?

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Two lines are parallel if they have the same slope but different y-intercepts, indicating that they will never intersect and thus represent an inconsistent system.

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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 of the line.