Readiness - Systems

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What is a system of equations?

Back

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 on a graph.

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

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A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

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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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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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How do you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the plot of the equations on a coordinate plane, where the intersection points represent the solutions.

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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 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 are parallel and do not intersect.

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What is the significance of the coefficients in a system of equations?

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The coefficients determine the slope and position of the lines represented by the equations, affecting their intersection and the nature of the solutions.

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How can you tell if two equations represent the same line?

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Two equations represent the same line if they are equivalent, meaning one can be transformed into the other through algebraic manipulation.