A1- 5.1 FLASHCARD Verifying Solutions 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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How do you verify if a point is a solution to a system of equations?

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

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What does it mean if a point satisfies both equations in a system?

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If a point satisfies both equations, it means that the point lies on the line represented by both equations, making it a solution to the system.

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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 intersection of the lines represented by each equation on a coordinate plane.

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

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

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

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A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How can you determine if a point is not a solution to a system of equations?

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A point is not a solution if substituting its coordinates into the equations does not satisfy at least one of the equations.

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What is the first step in solving a system of equations graphically?

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The first step is to graph each equation on the same coordinate plane to find the intersection point.

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What is substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.