Test System of Equations and Inequalities

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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 an ordered pair to be a solution to a system of equations?

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An ordered pair (x, y) is a solution to a system of equations if it satisfies all equations in the system when substituted for x and y.

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How do you determine if an ordered pair is a solution to a given equation?

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Substitute the x and y values of the ordered pair into the equation. If both sides of the equation are equal, then it 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 intersection point(s) of the lines represented by the equations on a coordinate plane.

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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 remaining 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 no points of intersection, indicating that the system has no solution.

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

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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How can you identify the solution of a system of equations graphically?

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The solution can be identified as the point where the graphs of the equations intersect.

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What is an inequality in the context of systems of equations?

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An inequality is a mathematical statement that compares two expressions, indicating that one is greater than, less than, or equal to the other.