Systems of Equations: Substitution

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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 to the system is the set of values that satisfy all equations simultaneously.

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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 when the equations represent parallel lines that never intersect.

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What does it mean if a system of equations has infinite solutions?

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A system of equations has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

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How do you solve a system of equations using substitution?

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To solve a system using substitution, solve one equation for one variable, then substitute that expression into the other equation.

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

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The first step is to isolate one variable in one of the equations.

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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 points of the lines represented by the equations.

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What does it indicate if two equations in a system are identical?

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If two equations in a system are identical, it indicates that there are infinite solutions, as they represent the same line.

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

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The point of intersection represents the solution to the system, where both equations are satisfied.

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How can you determine if a system of equations has one solution, no solution, or infinite solutions?

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You can determine this by analyzing the slopes and y-intercepts of the lines represented by the equations.

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What is the substitution method used for?

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The substitution method is used to solve systems of equations by replacing one variable with an expression derived from another equation.