Systems of Equations Review

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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 to solve a system of equations by graphing?

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To solve by graphing means to plot the equations on a graph and find the point(s) where they intersect.

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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 other variable.

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What are the possible types of solutions for a system of equations?

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1. One Solution: The lines intersect at one point. 2. No Solution: The lines are parallel and never intersect. 3. Infinitely Many Solutions: The lines are the same line.

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which have the same slope but different y-intercepts.

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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 does it mean if two equations are dependent?

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Dependent equations are equations that represent the same line, resulting in infinitely many solutions.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection points represent the solutions.

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How can you check your solution for a system of equations?

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

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

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The first step is to align the equations so that corresponding variables and constants are in the same columns.