Solve 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 are the methods to solve systems of equations?

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The main methods are: 1) Graphing, 2) Substitution, 3) Elimination.

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What is the elimination method?

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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 the substitution method?

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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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How do you graph a system of equations?

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To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where they intersect.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions.

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What is a consistent system of equations?

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A consistent system has at least one solution, which can be either one solution (intersecting lines) or infinitely many solutions (coinciding lines).

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, which occurs when the equations represent parallel lines.