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 are the methods to solve a system of equations?

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The main methods to solve a system of equations are substitution, elimination, and graphing.

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How do you solve a system of equations using substitution?

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

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What is the elimination method for 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 for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.

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How can you determine the number of solutions in a system of equations?

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You can determine the number of solutions by analyzing the slopes and intercepts of the lines represented by the equations.

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

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The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.

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How do you set up a system of equations from a word problem?

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Identify the variables, translate the relationships and conditions into equations, and then write them as a system.