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

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What does it mean to solve a system of equations graphically?

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To solve a system of equations graphically means to plot the equations on a graph and identify the point(s) where the lines intersect, which represent the solution(s) to the system.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of the variables.

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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 of equations 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 of equations has no solution, meaning the equations represent parallel lines that never intersect.

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What is the definition of dependent equations?

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Dependent equations are equations that represent the same line, meaning they have infinitely many solutions.

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How do you determine the solution of a system of equations using substitution?

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To determine the solution using substitution, isolate one variable in one equation, substitute that expression into the other equation, and solve for the remaining variable.

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

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The intersection point of a system of equations represents the values of the variables that satisfy all equations in the system.

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

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The first step in solving by elimination is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.