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 point(s) where the equations intersect.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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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 point(s) of the lines represented by the equations on a coordinate plane.

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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 other variable.

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What is a consistent system of equations?

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

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solution, meaning the lines are parallel and never intersect.

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What is a dependent system of equations?

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

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How do you determine the solution of a system of equations graphically?

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To determine the solution graphically, plot the equations on a coordinate plane and identify the point(s) where the lines intersect.

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What is the first step in solving the system: 3x + 2y = 16 and 7x + y = 19?

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The first step is to use either the substitution or elimination method to isolate one variable.