Solving 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 set of values that satisfy all equations in the system simultaneously.

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

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When two lines intersect, it means that there is a unique solution to the system of equations, represented by the point of intersection.

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What is the graphical method for solving systems of equations?

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The graphical method involves plotting the equations on a graph and identifying the point(s) where the lines 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 remaining variable.

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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 do you determine the solution of a system of equations algebraically?

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To determine the solution algebraically, you can use either the substitution or elimination method to find the values of the variables that satisfy all equations.

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What is the importance of the y-coordinate in a solution to a system of equations?

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The y-coordinate in a solution represents the value of the dependent variable when the equations are satisfied at the point of intersection.

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How can you check if a solution is correct for a system of equations?

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You can check if a solution is correct by substituting the values back into the original equations to see if they hold true.