8.9A Systems of Equations Checkpoint

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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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How do you find the solution to a system of equations graphically?

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To find the solution graphically, plot both equations on the same coordinate plane and identify the point(s) where the lines intersect.

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What does it mean for two lines to be parallel in a system of equations?

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If two lines are parallel, they have the same slope but different y-intercepts, meaning they will never intersect and have no solution.

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What does it mean for two lines to be 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 infinitely many solutions as every point on the line is a solution.

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What is the substitution method in solving systems of equations?

Back

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 remaining variable.

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What is an ordered pair in the context of systems of equations?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the coordinate plane, which can be a solution to a system of equations.

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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 ordered pair into both equations. If both equations are satisfied, the solution is correct.

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What is the significance of the intersection point of two lines in a system of equations?

Back

The intersection point represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

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

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A system has no solution if the lines are parallel, meaning they do not intersect at any point.